{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T01:08:07Z","timestamp":1772240887147,"version":"3.50.1"},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2009,5,30]],"date-time":"2009-05-30T00:00:00Z","timestamp":1243641600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mediterr. J. Math."],"published-print":{"date-parts":[[2009,7]]},"DOI":"10.1007\/s00009-009-0006-7","type":"journal-article","created":{"date-parts":[[2009,5,29]],"date-time":"2009-05-29T04:49:45Z","timestamp":1243572585000},"page":"215-232","source":"Crossref","is-referenced-by-count":22,"title":["Fractional and Hypersingular Operators in Variable Exponent Spaces on Metric Measure Spaces"],"prefix":"10.1007","volume":"6","author":[{"given":"Alexandre","family":"Almeida","sequence":"first","affiliation":[]},{"given":"Stefan","family":"Samko","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2009,5,30]]},"reference":[{"key":"6_CR1","first-page":"311","volume":"6","author":"A. Almeida","year":"2003","unstructured":"Almeida A.: Inversion of the Riesz potential operator on Lebesgue spaces with variable exponent. Fract. Calc. Appl. Anal. 6, 311\u2013327 (2003)","journal-title":"Fract. Calc. Appl. Anal."},{"key":"6_CR2","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1155\/2006\/610535","volume":"4","author":"A. Almeida","year":"2006","unstructured":"Almeida A., Samko S.: Characterization of Riesz and Bessel potentials on variable Lebesgue spaces. J. Funct. Spaces Appl. 4, 113\u2013144 (2006)","journal-title":"J. Funct. Spaces Appl."},{"issue":"no. 2","key":"6_CR3","doi-asserted-by":"crossref","first-page":"179","DOI":"10.4171\/ZAA\/1317","volume":"26","author":"A. Almeida","year":"2007","unstructured":"Almeida A., Samko S.: Pointwise inequalities in variable Sobolev spaces and applications. Z. Anal. Anwend. 26(no. 2), 179\u2013193 (2007)","journal-title":"Z. Anal. Anwend."},{"issue":"no. 2","key":"6_CR4","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1515\/GMJ.2008.195","volume":"15","author":"A. Almeida","year":"2008","unstructured":"Almeida A., Hasanov J., Samko S.: Maximal and potential operators in variable exponent Morrey spaces. Georgian Math. J. 15(no. 2), 195\u2013208 (2008)","journal-title":"Georgian Math. J."},{"key":"6_CR5","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/j.jmaa.2008.12.034","volume":"353","author":"A. Almeida","year":"2009","unstructured":"Almeida A., Samko S.: Embeddings of variable Haj\u0142asz-Sobolev spaces into H\u00f6lder spaces of variable order. J. Math. Anal. Appl. 353, 489\u2013496 (2009)","journal-title":"J. Math. Anal. Appl."},{"issue":"no. 1","key":"6_CR6","first-page":"77","volume":"106","author":"B. Bojarski","year":"1993","unstructured":"Bojarski B., Haj\u0142asz P.: Pointwise inequalities for Sobolev functions and some applications. Studia Math. 106(no. 1), 77\u201392 (1993)","journal-title":"Studia Math."},{"key":"6_CR7","doi-asserted-by":"crossref","unstructured":"R.R. Coifman and G. Weiss, Analyse harmonique non-commutative sur certaines espaces homegenes, Lecture Notes in Mathematics 242, Springer-Verlag, Berlin, 1971.","DOI":"10.1007\/BFb0058946"},{"issue":"no. 4","key":"6_CR8","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1090\/S0002-9904-1977-14325-5","volume":"83","author":"R.R. Coifman","year":"1977","unstructured":"Coifman R.R., Weiss G.: Extensions of Hardy spaces and their use in analysis. Bull. Amer. Math. Soc. 83(no. 4), 569\u2013645 (1977)","journal-title":"Bull. Amer. Math. Soc."},{"key":"6_CR9","first-page":"239","volume":"31","author":"D. Cruz-Uribe","year":"2006","unstructured":"Cruz-Uribe D., Fiorenza A., Martell J.M., P\u00e9rez C.: The boundedness of classical operators on variable L p spaces. Ann. Acad. Sci. Fenn. Math. 31, 239\u2013264 (2006)","journal-title":"Ann. Acad. Sci. Fenn. Math."},{"key":"6_CR10","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1002\/mana.200310157","volume":"268","author":"L. Diening","year":"2004","unstructured":"Diening L.: Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spaces L p(\u00b7) and W k,p(\u00b7). Math. Nachr. 268, 31\u201343 (2004)","journal-title":"Math. Nachr."},{"key":"6_CR11","unstructured":"L. Diening, P. H\u00e4st\u00f6 and A. Nekvinda, Open problems in variable exponent Lebesgue and Sobolev spaces, in: FSDONA 2004 Proceedings, P. Dr\u00e1bek, J. R\u00e1kosn\u00edk eds., Math. Inst. Acad. Sci. Czech Rep., Prague, 2005, 38\u201358."},{"key":"6_CR12","doi-asserted-by":"crossref","first-page":"681","DOI":"10.4171\/ZAA\/1102","volume":"21","author":"D.E. Edmunds","year":"2002","unstructured":"Edmunds D.E., Meskhi A.: Potential type operators in L p(x) spaces. Z. Anal. Anwendungen 21, 681\u2013690 (2002)","journal-title":"Z. Anal. Anwendungen"},{"key":"6_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-9922-1","volume-title":"Bounded and Compact Integral Operators, Mathematics and its Applications 543","author":"D.E. Edmunds","year":"2002","unstructured":"Edmunds D.E., Kokilashvili V., Meskhi A.: Bounded and Compact Integral Operators, Mathematics and its Applications 543. Kluwer Academic Publishers, Dordrecht (2002)"},{"issue":"no. 2","key":"6_CR14","first-page":"495","volume":"31","author":"T. Futamura","year":"2006","unstructured":"Futamura T., Mizuta Y., Shimomura T.: Sobolev embeddings for variable exponent Riesz potentials on metric spaces. Ann. Acad. Sci. Fenn. Math. 31(no. 2), 495\u2013522 (2006)","journal-title":"Ann. Acad. Sci. Fenn. Math."},{"key":"6_CR15","doi-asserted-by":"crossref","first-page":"245","DOI":"10.4064\/sm162-3-5","volume":"162","author":"J. Garc\u00eda-Cuerva","year":"2004","unstructured":"Garc\u00eda-Cuerva J., Gatto A.E.: Boundedness properties of fractional integral operators associated to non-doubling measures. Studia Math. 162, 245\u2013261 (2004)","journal-title":"Studia Math."},{"key":"6_CR16","doi-asserted-by":"crossref","unstructured":"A.E., Gatto, On fractional calculus associated to doubling and non-doubling measures, in: Harmonic analysis: Calderon-Zygmund and beyond, J.M. Ash et\u00a0al. eds., Contemp. Math. 411, Amer. Math. Soc., Providence, RI, 2006, 15\u201337.","DOI":"10.1090\/conm\/411\/07745"},{"issue":"no. 1","key":"6_CR17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4171\/rmi\/196","volume":"12","author":"A.E. Gatto","year":"1996","unstructured":"Gatto A.E., Segovia C., Vagi S.: On fractional differentiation on spaces of homogeneous type. Rev. Mat. Iberoamericana 12(no. 1), 1\u201335 (1996)","journal-title":"Rev. Mat. Iberoamericana"},{"key":"6_CR18","unstructured":"I. Genebashvili, A. Gogatishvili, V. Kokilashvili and M. Krbec, Weight Theory for Integral Transforms on Spaces of Homogeneous Type, Pitman Monographs and Surveys in Pure and Applied Mathematics 92, Longman Scientific and Technical, Harlow, 1998."},{"key":"6_CR19","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1007\/BF00275475","volume":"5","author":"P. Haj\u0142asz","year":"1996","unstructured":"Haj\u0142asz P.: Sobolev spaces on arbitrary metric spaces. Potential Anal. 5, 403\u2013415 (1996)","journal-title":"Potential Anal."},{"issue":"no. 3","key":"6_CR20","doi-asserted-by":"crossref","first-page":"601","DOI":"10.4171\/RMI\/246","volume":"14","author":"P. Haj\u0142asz","year":"1998","unstructured":"Haj\u0142asz P., Kinnunen J.: H\u00f6lder quasicontinuity of Sobolev functions on metric spaces. Rev. Mat. Iberoamericana 14(no. 3), 601\u2013622 (1998)","journal-title":"Rev. Mat. Iberoamericana"},{"key":"6_CR21","doi-asserted-by":"crossref","unstructured":"P. Haj\u0142asz and P. Koskela, Sobolev met Poincar\u00e9, Mem. Amer. Math. Soc. 145, no. 688, 2000.","DOI":"10.1090\/memo\/0688"},{"key":"6_CR22","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1006\/jfan.1996.2959","volume":"143","author":"P. Haj\u0142asz","year":"1997","unstructured":"Haj\u0142asz P., Martio O.: Traces of Sobolev functions on fractal type sets and characterization of extension domains. J. Funct. Anal. 143, 221\u2013246 (1997)","journal-title":"J. Funct. Anal."},{"issue":"no. 3","key":"6_CR23","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1007\/s00209-006-0960-8","volume":"254","author":"P. Harjulehto","year":"2006","unstructured":"Harjulehto P., H\u00e4st\u00f6 P., Latvala V.: Sobolev embeddings in metric measure spaces with variable dimension. Math. Z. 254(no. 3), 591\u2013609 (2006)","journal-title":"Math. Z."},{"key":"6_CR24","doi-asserted-by":"crossref","first-page":"87","DOI":"10.14321\/realanalexch.30.1.0087","volume":"30","author":"P. Harjulehto","year":"2004\/05","unstructured":"Harjulehto P., H\u00e4st\u00f6 P., Pere M.: Variable exponent Lebesgue spaces on metric spaces: the Hardy-Littlewood maximal operator. Real Anal. Exchange 30, 87\u2013104 (2004\/05)","journal-title":"Real Anal. Exchange"},{"key":"6_CR25","doi-asserted-by":"crossref","first-page":"79","DOI":"10.7169\/facm\/1229616443","volume":"36","author":"P. Harjulehto","year":"2006","unstructured":"Harjulehto P., H\u00e4st\u00f6 P., Pere M.: Variable exponent Sobolev spaces on metric measure spaces. Funct. Approx. Comment. Math. 36, 79\u201394 (2006)","journal-title":"Funct. Approx. Comment. Math."},{"key":"6_CR26","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-0131-8","volume-title":"Lectures on Analysis on Metric Spaces","author":"J. Heinonen","year":"2001","unstructured":"Heinonen J.: Lectures on Analysis on Metric Spaces. Springer-Verlag, New York (2001)"},{"key":"6_CR27","first-page":"17","volume":"138","author":"M. Khabazi","year":"2005","unstructured":"Khabazi M.: The maximal operator in spaces of homogeneous type. Proc. A. Razmadze Math. Inst. 138, 17\u201325 (2005)","journal-title":"Proc. A. Razmadze Math. Inst."},{"issue":"no. 4","key":"6_CR28","doi-asserted-by":"crossref","first-page":"489","DOI":"10.4310\/MRL.1997.v4.n4.a6","volume":"4","author":"J. Kinnunen","year":"1997","unstructured":"Kinnunen J., Martio O.: Hardy\u2019s inequalities for Sobolev functions. Math. Res. Lett. 4(no. 4), 489\u2013500 (1997)","journal-title":"Math. Res. Lett."},{"key":"6_CR29","unstructured":"V. Kokilashvili, On a progress in the theory of integral operators in weighted Banach function spaces, in: FSDONA 2004 Proceedings, P. Dr\u00e1bek, J. R\u00e1kosn\u00edk eds., Math. Inst. Acad. Sci. Czech Rep., Prague, 2005, 152\u2013175."},{"key":"6_CR30","first-page":"1","volume":"4","author":"V. Kokilashvili","year":"2001","unstructured":"Kokilashvili V., Meskhi A.: Fractional integrals on measure spaces. Fract. Calc. Appl. Anal. 4, 1\u201324 (2001)","journal-title":"Fract. Calc. Appl. Anal."},{"key":"6_CR31","doi-asserted-by":"crossref","first-page":"871","DOI":"10.4171\/ZAA\/1272","volume":"24","author":"V. Kokilashvili","year":"2005","unstructured":"Kokilashvili V., Meskhi A.: On some weighted inequalities for fractional integrals on nonhomogeneous spaces. Z. Anal. Anwendungen 24, 871\u2013885 (2005)","journal-title":"Z. Anal. Anwendungen"},{"key":"6_CR32","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1080\/10652460701445344","volume":"18","author":"V. Kokilashvili","year":"2007","unstructured":"Kokilashvili V., Meskhi A.: Weighted criteria for generalized fractional maximal functions and potentials in Lebesgue spaces with variable exponent. Integral Transforms Spec. Funct. 18, 609\u2013628 (2007)","journal-title":"Integral Transforms Spec. Funct."},{"key":"6_CR33","doi-asserted-by":"crossref","first-page":"899","DOI":"10.4171\/ZAA\/1178","volume":"22","author":"V. Kokilashvili","year":"2003","unstructured":"Kokilashvili V., Samko S.: On Sobolev Theorem for Riesz type potentials in the Lebesgue spaces with variable exponent. Z. Anal. Anwendungen 22, 899\u2013910 (2003)","journal-title":"Z. Anal. Anwendungen"},{"key":"6_CR34","doi-asserted-by":"crossref","first-page":"493","DOI":"10.4171\/RMI\/398","volume":"20","author":"V. Kokilashvili","year":"2004","unstructured":"Kokilashvili V., Samko S.: Maximal and fractional operators in weighted L p(x) spaces. Rev. Mat. Iberoamericana 20, 493\u2013515 (2004)","journal-title":"Rev. Mat. Iberoamericana"},{"key":"6_CR35","first-page":"137","volume":"144","author":"V. Kokilashvili","year":"2007","unstructured":"Kokilashvili V., Samko S.: The maximal operator in weighted variable spaces on metric measure spaces. Proc. A. Razmadze Math. Inst. 144, 137\u2013144 (2007)","journal-title":"Proc. A. Razmadze Math. Inst."},{"issue":"4","key":"6_CR36","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1515\/GMJ.2008.683","volume":"15","author":"V. Kokilashvili","year":"2008","unstructured":"Kokilashvili V., Samko S: The maximal operator in weighted variable spaces on metric spaces. Georgian Math. J. 15(4), 683\u2013712 (2008)","journal-title":"Georgian Math. J."},{"issue":"11","key":"6_CR37","doi-asserted-by":"crossref","first-page":"1775","DOI":"10.1007\/s10114-008-6464-1","volume":"24","author":"V. Kokilashvili","year":"2008","unstructured":"Kokilashvili V., Samko S.: Boundedness of maximal operators and potential operators on Carleson curves in Lebesgue spaces with variable exponent. Acta Math. Sin. 24(11), 1775\u20131800 (2008)","journal-title":"Acta Math. Sin."},{"key":"6_CR38","first-page":"109","volume":"145","author":"V. Kokilashvili","year":"2007","unstructured":"Kokilashvili V., Samko S.: A general approach to weighted boundedness of operators of harmonic analysis in variable exponent Lebesgue spaces. Proc. A. Razmadze Math. Inst. 145, 109\u2013116 (2007)","journal-title":"Proc. A. Razmadze Math. Inst."},{"issue":"1","key":"6_CR39","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.jmaa.2008.06.056","volume":"352","author":"V. Kokilashvili","year":"2009","unstructured":"Kokilashvili V., Samko S.: Operators of harmonic analysis in weighted spaces with non-standard growth. J. Math. Anal. Appl., 352(1), 15\u201334 (2009)","journal-title":"J. Math. Anal. Appl.,"},{"issue":"116","key":"6_CR40","doi-asserted-by":"crossref","first-page":"592","DOI":"10.21136\/CMJ.1991.102493","volume":"41","author":"O. Kova\u030cci\u030ck","year":"1991","unstructured":"Kova\u030cci\u030ck O., R\u00e1kosn\u00edk J.: On spaces L p(x) and W k,p(x). Czechoslovak Math. J. 41(116), 592\u2013618 (1991)","journal-title":"Czechoslovak Math. J."},{"key":"6_CR41","doi-asserted-by":"crossref","first-page":"96","DOI":"10.3792\/pjaa.80.96","volume":"80","author":"Y. Mizuta","year":"2004","unstructured":"Mizuta Y., Shimomura T.: Continuity of Sobolev functions of variable exponent on metric spaces. Proc. Japan Acad. Ser. A Math. Sci. 80, 96\u201399 (2004)","journal-title":"Proc. Japan Acad. Ser. A Math. Sci."},{"issue":"1","key":"6_CR42","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1016\/j.jmaa.2005.02.046","volume":"311","author":"Y. Mizuta","year":"2005","unstructured":"Mizuta Y., Shimomura T.: Sobolev\u2019s inequality for Riesz potentials with variable exponent satisfying a log-H\u00f6lder condition at infinity. J.Math. Anal. Appl. 311(1), 268\u2013288 (2005)","journal-title":"J.Math. Anal. Appl."},{"key":"6_CR43","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4064\/sm176-1-1","volume":"176","author":"E. Nakai","year":"2006","unstructured":"Nakai E.: The Campanato, Morrey and H\u00f6lder spaces on spaces of homogeneous type. Studia Math. 176, 1\u201319 (2006)","journal-title":"Studia Math."},{"issue":"4","key":"6_CR44","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1155\/S0161171295001001","volume":"18","author":"B. Ross","year":"1995","unstructured":"Ross B., Samko S.: Fractional integration operator of variable order in the spaces H \u03bb . Internat. J. Math. Math. Sci. 18(4), 777\u2013788 (1995)","journal-title":"Internat. J. Math. Math. Sci."},{"key":"6_CR45","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1080\/10652469808819204","volume":"7","author":"S. Samko","year":"1998","unstructured":"Samko S.: Convolution and potential type operators in L p(x) ( $${\\mathbb{R}^n}$$ ). Integral Transforms Spec. Funct. 7, 261\u2013284 (1998)","journal-title":"Integral Transforms Spec. Funct."},{"issue":"3","key":"6_CR46","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/BF01911126","volume":"21","author":"S. Samko","year":"1995","unstructured":"Samko S.: Fractional integration and differentiation of variable order. Anal. Math. 21(3), 213\u2013236 (1995)","journal-title":"Anal. Math."},{"key":"6_CR47","doi-asserted-by":"crossref","unstructured":"S.G. Samko, Hypersingular Integrals and Their Applications, Analytical Methods and Special Functions 4, Taylor & Francis Ltd., London, 2002","DOI":"10.1201\/9781482264968"},{"key":"6_CR48","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1080\/10652460412331320322","volume":"16","author":"S. Samko","year":"2005","unstructured":"Samko S.: On a progress in the theory of Lebesgue spaces with variable exponent: maximal and singular operators. Integral Transforms Spec. Funct. 16, 461\u2013482 (2005)","journal-title":"Integral Transforms Spec. Funct."},{"key":"6_CR49","volume-title":"Fractional Integrals and Derivatives. Theory and Applications","author":"S. Samko","year":"1993","unstructured":"Samko S., Kilbas A., Marichev O.: Fractional Integrals and Derivatives. Theory and Applications. Gordon and Breach Science Publishers, Yverdon (1993)"}],"container-title":["Mediterranean Journal of Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00009-009-0006-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00009-009-0006-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00009-009-0006-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,13]],"date-time":"2024-03-13T23:18:41Z","timestamp":1710371921000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00009-009-0006-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,5,30]]},"references-count":49,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2009,7]]}},"alternative-id":["6"],"URL":"https:\/\/doi.org\/10.1007\/s00009-009-0006-7","relation":{},"ISSN":["1660-5446","1660-5454"],"issn-type":[{"value":"1660-5446","type":"print"},{"value":"1660-5454","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,5,30]]}}}