{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T15:51:23Z","timestamp":1774626683876,"version":"3.50.1"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2016,6,1]],"date-time":"2016-06-01T00:00:00Z","timestamp":1464739200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2016,6,1]],"date-time":"2016-06-01T00:00:00Z","timestamp":1464739200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["FCAA"],"published-print":{"date-parts":[[2016,6]]},"DOI":"10.1515\/fca-2016-0033","type":"journal-article","created":{"date-parts":[[2016,7,14]],"date-time":"2016-07-14T11:29:51Z","timestamp":1468495791000},"page":"608-624","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Riesz Fractional Integrals in Grand Lebesgue Spaces on \u211dn"],"prefix":"10.1007","volume":"19","author":[{"given":"Stefan","family":"Samko","sequence":"first","affiliation":[]},{"given":"Salaudin","family":"Umarkhadzhiev","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,6,28]]},"reference":[{"key":"190303_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-9922-1","volume-title":"Bounded and Compact Integral Operators Volume 543 of Mathematics and its Applications","author":"DE Edmunds","year":"2002","unstructured":"D.E. Edmunds, V. Kokilashvili, A. Meskhi, Bounded and Compact Integral Operators Volume 543 of Mathematics and its Applications. Kluwer Academic Publishers, Dordrecht (2002)."},{"issue":"2","key":"190303_CR2","doi-asserted-by":"publisher","first-page":"123","DOI":"10.4064\/sm188-2-2","volume":"188","author":"A Fiorenza","year":"2008","unstructured":"A. Fiorenza, B. Gupta, P. Jain, The maximal theorem in weighted grand Lebesgue spaces. Studia Math. 188, No 2, (2008), 123\u2013133.","journal-title":"Studia Math."},{"key":"190303_CR3","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1007\/BF02678192","volume":"92","author":"L Greco","year":"1997","unstructured":"L. Greco, T. Iwaniec, C. Sbordone, Inverting the p-harmonic operator. Manuscripta Math. 92 (1997), 249\u2013258.","journal-title":"Manuscripta Math."},{"issue":"5","key":"190303_CR4","doi-asserted-by":"publisher","first-page":"1128","DOI":"10.1515\/fca-2015-0065","volume":"18","author":"Z Hao","year":"2015","unstructured":"Z. Hao, Y. Jiao, Fractional integral on martingale hardy spaces with variable exponents. Fract. Calc. Appl. Anal. 18, No 5, (2015), 1128\u2013114; DOI: 10.1515\/fca-2015-0065; http:\/\/www.degruyter.com\/view\/j\/fca.2015.18.issue-5\/issue-files\/fca.2015.18.issue-5.xml","journal-title":"Fract. Calc. Appl. Anal."},{"key":"190303_CR5","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/BF00375119","volume":"119","author":"T Iwaniec","year":"1992","unstructured":"T. Iwaniec, C. Sbordone, On the integrability of the Jacobian under minimal hypotheses. Arch. Rational Mech. Anal. 119 (1992), 129\u2013143.","journal-title":"Arch. Rational Mech. Anal."},{"issue":"2","key":"190303_CR6","first-page":"639","volume":"328","author":"R Johnson","year":"1991","unstructured":"R. Johnson, C.J. Neugebauer, Change of variables results for - and reverse H\u00f6lder -classes. Trans. Amer. Math. Soc. 328, No 2, (1991), 639\u2013666.","journal-title":"Trans. Amer. Math. Soc."},{"key":"190303_CR7","doi-asserted-by":"publisher","first-page":"3","DOI":"10.5565\/PUBLMAT_57113_01","volume":"57","author":"A Kairema","year":"2013","unstructured":"A. Kairema, Two-weight norm inequalities for potential type and maximal operators in a metric space. Publ. Mat. 57 (2013), 3\u201356.","journal-title":"Publ. Mat."},{"issue":"4","key":"190303_CR8","first-page":"437","volume":"7","author":"NK Karapetiants","year":"2004","unstructured":"N.K. Karapetiants, N.G. Samko, Weighted theorems onfractional integrals in the generalized H\u00f6lder spaces via the indices and. Fract. Calc. Appl. Anal. 7, No 4, (2004), 437\u2013458.","journal-title":"Fract. Calc. Appl. Anal."},{"issue":"1","key":"190303_CR9","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1007\/s10958-010-0076-x","volume":"170","author":"V Kokilashvili","year":"2010","unstructured":"V. Kokilashvili, Boundedness criteria for singular integrals in weighted Grand Lebesgue spaces. J. Math. Sci. 170, No 1, (2010), 20\u201333.","journal-title":"J. Math. Sci."},{"issue":"5","key":"190303_CR10","doi-asserted-by":"publisher","first-page":"1146","DOI":"10.1515\/fca-2015-0066","volume":"18","author":"V Kokilashvili","year":"2015","unstructured":"V. Kokilashvili, M. Mastylo, A. Meskhi, Two-weight norm estimates for multilinear fractional integrals in classical lebesgue spaces. Fract. Calc. Appl. Anal. 18, No 5, (2015), 1146\u20131163; DOI: 10.1515\/fca-2015-0066; http:\/\/www.degruyter.com\/view\/j\/fca.2015.18.issue-5\/ issue-files\/fca.2015.18.issue-5.xml","journal-title":"Fract. Calc. Appl. Anal."},{"issue":"1","key":"190303_CR11","first-page":"1","volume":"4","author":"V Kokilashvili","year":"2001","unstructured":"V. Kokilashvili, A. Meskhi, Fractional integrals on measure spaces. Fract. Calc. Appl. Anal. 4, No 1, (2001), 1\u201324.","journal-title":"Fract. Calc. Appl. Anal."},{"issue":"3","key":"190303_CR12","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1515\/GMJ.2009.547","volume":"16","author":"V Kokilashvili","year":"2009","unstructured":"V. Kokilashvili, A. Meskhi, A note on the boundedness of the Hilberttransform in weighted grand Lebesgue spaces. Georgian Math. J. 16, No 3, (2009), 547\u2013551.","journal-title":"Georgian Math. J."},{"issue":"2","key":"190303_CR13","doi-asserted-by":"publisher","first-page":"159","DOI":"10.4064\/sm210-2-4","volume":"210","author":"V Kokilashvili","year":"2012","unstructured":"V. Kokilashvili, A. Meskhi, Trace inequalities for fractional integrals in grand Lebesgue spaces. Studia Math. 210, No 2, (2012), 159\u2013176.","journal-title":"Studia Math."},{"issue":"1","key":"190303_CR14","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/s10986-013-9191-y","volume":"53","author":"V Kokilashvili","year":"2013","unstructured":"V. Kokilashvili, A. Meskhi, Potentials with product kernels in grand Lebesgue spaces: One-weight criteria. Lithuanian Mathematical Journal. 53, No 1, (2013), 27\u201339.","journal-title":"Lithuanian Mathematical Journal."},{"key":"190303_CR15","volume-title":"Integral Operators in Non-standard Function Spaces, I and II","author":"V Kokilashvili","year":"2016","unstructured":"V. Kokilashvili, A. Meskhi, H. Rafeiro, S. Samko, Integral Operators in Non-standard Function Spaces, I and II. Springer-Birkh\u00e4ser (2016)."},{"issue":"1","key":"190303_CR16","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1515\/GMJ.2003.145","volume":"10","author":"V Kokilashvili","year":"2003","unstructured":"V. Kokilashvili, S. Samko, Singular integrals in weighted Lebesgue spaces with variable exponent. Georgian Math. J. 10, No 1, (2003), 145\u2013156.","journal-title":"Georgian Math. J."},{"key":"190303_CR17","volume-title":"Orlicz Spaces and Interpolation. Dept. de Matem\u00e1tica","author":"L Maligranda","year":"1989","unstructured":"L. Maligranda, Orlicz Spaces and Interpolation. Dept. de Matem\u00e1tica. Univ. Estadual de Campinas, Campinas SP Brazil (1989)."},{"key":"190303_CR18","volume-title":"arXiv:1007.1185","author":"A Meskhi","year":"2010","unstructured":"A. Meskhi, Criteria for the boundedness of potential operators in grand Lebesgue spaces. arXiv:1007.1185 (2010)."},{"issue":"6","key":"190303_CR19","doi-asserted-by":"publisher","first-page":"622","DOI":"10.1007\/s10958-011-0574-5","volume":"178","author":"A Meskhi","year":"2011","unstructured":"A. Meskhi, Weighted criteria for the Hardy transform under the bp condition in grand lebesgue spaces and some applications. J. Math. Sci. 178, No 6, (2011), 622\u2013636.","journal-title":"J. Math. Sci."},{"key":"190303_CR20","doi-asserted-by":"crossref","unstructured":"N. Samko, Weighted Hardy and potential operators in Morrey spaces. J. Funct. Spaces Appl. 2012 (2012), 21 pp.","DOI":"10.1155\/2012\/678171"},{"issue":"3","key":"190303_CR21","doi-asserted-by":"publisher","first-page":"683","DOI":"10.1007\/s11117-012-0199-z","volume":"17","author":"N Samko","year":"2013","unstructured":"N. Samko, Weighted Hardy operators in the local generalized vanishing Morrey spaces. Positivity. 17, No 3, (2013), 683\u2013706.","journal-title":"Positivity."},{"key":"190303_CR22","doi-asserted-by":"crossref","unstructured":"S.G. Samko, Hypersingular Integrals and their Applications. Ser. \u201c Analytical Methods and Special Functions\u201d. 5, Taylor & Francis, London-New-York (2002).","DOI":"10.1201\/9781482264968"},{"issue":"2","key":"190303_CR23","doi-asserted-by":"publisher","first-page":"370","DOI":"10.2478\/s13540-013-0023-x","volume":"16","author":"SG Samko","year":"2013","unstructured":"S.G. Samko, A note on Riesz fractional integrals in the limiting case \u03b1(x)px)\u2261n Fract. Calc. Appl. Anal. 16, No 2, (2013), 370\u2013377; DOI: 10.2478\/s13540-013-0023-x; http:\/\/www.degruyter.com\/view\/j\/fca.2013.16.issue-2\/issue-files\/fca.2013.16.issue-2.xml","journal-title":"A note on Riesz fractional integrals in the limiting case \u03b1(x)px)\u2261n Fract. Calc. Appl. Anal."},{"key":"190303_CR24","volume-title":"Fractional Integrals and Derivatives. Theory and Applications","author":"SG Samko","year":"1993","unstructured":"S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives. Theory and Applications. Gordon & Breach. Sci. Publ, London-New-York (1993) (Russian Ed.: Fractional Integrals and Derivatives and some of their Applications, Nauka i Tekhnika, Minsk, 1987)."},{"issue":"1","key":"190303_CR25","first-page":"67","volume":"1","author":"SG Samko","year":"2011","unstructured":"S.G. Samko, S.M. Umarkhadzhiev, On Iwaniec-Sbordone spaces on sets which may have infinite measure. Azerb. J. Math. 1, No 1, (2011), 67\u201384.","journal-title":"Azerb. J. Math."},{"issue":"4","key":"190303_CR26","doi-asserted-by":"publisher","first-page":"813","DOI":"10.2307\/2374799","volume":"114","author":"ET Sawyer","year":"1992","unstructured":"E.T. Sawyer, R.L. Weeden, Weighted inequalities for fractional integrals on euclidean and homogeneous spaces. Amer. J. Math. 114, No 4, (1992), 813\u2013874.","journal-title":"Amer. J. Math."},{"key":"190303_CR27","volume-title":"Singular Integrals and Differentiability Properties of Functions","author":"EM Stein","year":"1970","unstructured":"E.M. Stein, Singular Integrals and Differentiability Properties of Functions. Princeton Univ. Press (1970)."},{"key":"190303_CR28","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1090\/S0002-9947-1958-0092943-6","volume":"87","author":"EM Stein","year":"1958","unstructured":"E.M. Stein, G. Weiss, Interpolation of operators with change of measures. Trans. Amer. Math. Soc. 87 (1958), 159\u2013172.","journal-title":"Trans. Amer. Math. Soc."},{"issue":"2","key":"190303_CR29","first-page":"5","volume":"19","author":"SM Umarkhadzhiev","year":"2013","unstructured":"S.M. Umarkhadzhiev, Boundedness of linear operators in wieghted generalized grand Lebesgue spaces (In Russian). Vestnik of Chechen Academy of Sciences. 19, No 2, (2013), 5\u20139.","journal-title":"Vestnik of Chechen Academy of Sciences."},{"issue":"4","key":"190303_CR30","doi-asserted-by":"publisher","first-page":"35","DOI":"10.3103\/S1066369X14040057","volume":"58","author":"SM Umarkhadzhiev","year":"2014","unstructured":"S.M. Umarkhadzhiev, Generalization of the notion of grand Lebesgue space. Russian Mathematics (Izv. VUZ). 58, No 4, (2014), 35\u201343.","journal-title":"Russian Mathematics (Izv. VUZ)."}],"container-title":["Fractional Calculus and Applied Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/fca-2016-0033\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1515\/fca-2016-0033.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1515\/fca-2016-0033\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/fca-2016-0033\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1515\/fca-2016-0033.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,20]],"date-time":"2022-06-20T07:01:05Z","timestamp":1655708465000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1515\/fca-2016-0033"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6]]},"references-count":30,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,6]]}},"alternative-id":["190303"],"URL":"https:\/\/doi.org\/10.1515\/fca-2016-0033","relation":{},"ISSN":["1311-0454","1314-2224"],"issn-type":[{"value":"1311-0454","type":"print"},{"value":"1314-2224","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,6]]},"assertion":[{"value":"26 November 2015","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 June 2016","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}