{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T23:53:42Z","timestamp":1767138822810,"version":"build-2238731810"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2022,5,18]],"date-time":"2022-05-18T00:00:00Z","timestamp":1652832000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,5,18]],"date-time":"2022-05-18T00:00:00Z","timestamp":1652832000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Fourier Anal Appl"],"published-print":{"date-parts":[[2022,6]]},"DOI":"10.1007\/s00041-022-09940-8","type":"journal-article","created":{"date-parts":[[2022,5,18]],"date-time":"2022-05-18T16:03:36Z","timestamp":1652889816000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Maximal Operator in Variable Stummel Spaces"],"prefix":"10.1007","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3794-7831","authenticated-orcid":false,"given":"Alexandre","family":"Almeida","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5304-8572","authenticated-orcid":false,"given":"Humberto","family":"Rafeiro","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,5,18]]},"reference":[{"issue":"2","key":"9940_CR1","doi-asserted-by":"publisher","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(2), 195\u2013208 (2008). https:\/\/doi.org\/10.1515\/GMJ.2008.195","journal-title":"Georgian Math. J."},{"key":"9940_CR2","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/j.na.2017.08.006","volume":"164","author":"A Almeida","year":"2017","unstructured":"Almeida, A., Samko, S.: Embeddings of local generalized Morrey spaces between weighted Lebesgue spaces. Nonlinear Anal. 164, 67\u201376 (2017). https:\/\/doi.org\/10.1016\/j.na.2017.08.006","journal-title":"Nonlinear Anal."},{"issue":"3","key":"9940_CR3","doi-asserted-by":"publisher","first-page":"743","DOI":"10.4171\/RMI\/511","volume":"23","author":"C Capone","year":"2007","unstructured":"Capone, C., Cruz-Uribe, D., Fiorenza, A.: The fractional maximal operator and fractional integrals on variable $$L^p$$ spaces. Rev. Mat. Iberoam. 23(3), 743\u2013770 (2007). https:\/\/doi.org\/10.4171\/RMI\/511","journal-title":"Rev. Mat. Iberoam."},{"issue":"3","key":"9940_CR4","doi-asserted-by":"publisher","first-page":"361","DOI":"10.2478\/s13540-011-0023-7","volume":"14","author":"D Cruz-Uribe","year":"2011","unstructured":"Cruz-Uribe, D., Diening, L., H\u00e4st\u00f6, P.: The maximal operator on weighted variable Lebesgue spaces. Fract. Calc. Appl. Anal. 14(3), 361\u2013374 (2011). https:\/\/doi.org\/10.2478\/s13540-011-0023-7","journal-title":"Fract. Calc. Appl. Anal."},{"key":"9940_CR5","doi-asserted-by":"publisher","unstructured":"Cruz-Uribe, D., Fiorenza, A.: Variable Lebesgue spaces. In: Foundations and Harmonic Analysis. Birkh\u00e4user, 2013, 10\u2013312. https:\/\/doi.org\/10.1007\/978-3-0348-0548-3","DOI":"10.1007\/978-3-0348-0548-3"},{"issue":"2","key":"9940_CR6","doi-asserted-by":"publisher","first-page":"744","DOI":"10.1016\/j.jmaa.2012.04.044","volume":"394","author":"D Cruz-Uribe","year":"2012","unstructured":"Cruz-Uribe, D., Fiorenza, A., Neugebauer, C.J.: Weighted norm inequalities for the maximal operator on variable Lebesgue spaces. J. Math. Anal. Appl. 394(2), 744\u2013760 (2012). https:\/\/doi.org\/10.1016\/j.jmaa.2012.04.044","journal-title":"J. Math. Anal. Appl."},{"issue":"2","key":"9940_CR7","doi-asserted-by":"publisher","first-page":"245","DOI":"10.7153\/mia-07-27","volume":"7","author":"L Diening","year":"2004","unstructured":"Diening, L.: Maximal function on generalized Lebesgue spaces $$L^{p(\\cdot )}$$. Math. Inequal. Appl. 7(2), 245\u2013253 (2004). https:\/\/doi.org\/10.7153\/mia-07-27","journal-title":"Math. Inequal. Appl."},{"key":"9940_CR8","doi-asserted-by":"publisher","unstructured":"Diening, L., Harjulehto, P., H\u00e4st\u00f6, P., Ru\u017ei\u010dka, M.: Lebesgue and Sobolev Spaces with Variable Exponents. Lecture Notes in Mathematics, 2017th edn., pp. 10\u2013509. Springer, New York (2011). https:\/\/doi.org\/10.1007\/978-3-642-18363-8","DOI":"10.1007\/978-3-642-18363-8"},{"key":"9940_CR9","doi-asserted-by":"crossref","unstructured":"Diening, L., H\u00e4st\u00f6, P.: Muckenhoupt weights in variable exponent spaces. preprint (2010)","DOI":"10.1007\/978-3-642-18363-8_3"},{"key":"9940_CR10","unstructured":"Duoandikoetxea, J.: Fourier Analysis. Graduate Studies in Mathematics, 29th edn., pp. 18\u2013222. American Mathematical Society, Providence (2001)"},{"issue":"6","key":"9940_CR11","first-page":"1053","volume":"29","author":"GH Eridani","year":"2005","unstructured":"Eridani, G.H.: Stummel class of Morrey spaces. Southeast Asian Bull. Math. 29(6), 1053\u20131056 (2005)","journal-title":"Southeast Asian Bull. Math."},{"key":"9940_CR12","doi-asserted-by":"publisher","first-page":"107","DOI":"10.2307\/2373450","volume":"93","author":"C Fefferman","year":"1971","unstructured":"Fefferman, C., Stein, E.M.: Some maximal inequalities. Am. J. Math. 93, 107\u2013115 (1971). https:\/\/doi.org\/10.2307\/2373450","journal-title":"Am. J. Math."},{"key":"9940_CR13","unstructured":"Garc\u00eda-Cuerva, J., de Francia, R.J.L.: Weighted Norm Inequalities and Related Topics, pp. 10\u2013604. North-Holland, Amsterdam (1985)"},{"issue":"3","key":"9940_CR14","doi-asserted-by":"publisher","first-page":"1151","DOI":"10.1007\/s00009-015-0561-z","volume":"13","author":"VS Guliyev","year":"2016","unstructured":"Guliyev, V.S., Samko, S.G.: Maximal operator in variable exponent generalized Morrey spaces on quasi-metric measure space. Mediterr. J. Math. 13(3), 1151\u20131165 (2016). https:\/\/doi.org\/10.1007\/s00009-015-0561-z","journal-title":"Mediterr. J. Math."},{"issue":"8\u201310","key":"9940_CR15","doi-asserted-by":"publisher","first-page":"923","DOI":"10.1080\/17476930903276068","volume":"55","author":"V Kokilashvili","year":"2010","unstructured":"Kokilashvili, V., Meskhi, A.: Maximal functions and potentials in variable exponent Morrey spaces with non-doubling measure. Complex Var. Elliptic Equ. 55(8\u201310), 923\u2013936 (2010). https:\/\/doi.org\/10.1080\/17476930903276068","journal-title":"Complex Var. Elliptic Equ."},{"key":"9940_CR16","doi-asserted-by":"publisher","unstructured":"Kokilashvili, V., Meskhi, A., Rafeiro, H., Rafeiro, S.: Integral Operators in Non-standard Function Spaces. Volume 1: Variable Exponent Lebesgue and Amalgam Spaces, 248th edn., pp. 20\u2013567. Birkh\u00e4user, Basel (2016). https:\/\/doi.org\/10.1007\/978-3-319-21015-5","DOI":"10.1007\/978-3-319-21015-5"},{"key":"9940_CR17","doi-asserted-by":"publisher","unstructured":"Kokilashvili, V., Meskhi, A., Rafeiro, H., Samko, S.: Integral Operators in Non-standard Function Spaces. Volume 2: Variable Exponent H\u00f6lder, Morrey\u2013Campanato and Grand Spaces, 249th edn., pp. 571\u20131003. Birkh\u00e4user\/Springer, Basel (2016). https:\/\/doi.org\/10.1007\/978-3-319-21018-6","DOI":"10.1007\/978-3-319-21018-6"},{"issue":"3","key":"9940_CR18","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1155\/2007\/914143","volume":"5","author":"V Kokilashvili","year":"2007","unstructured":"Kokilashvili, V., Samko, N., Samko, S.: The maximal operator in weighted variable spaces $$L^{p(\\cdot )}$$. J. Funct. Spaces Appl. 5(3), 299\u2013317 (2007). https:\/\/doi.org\/10.1155\/2007\/914143","journal-title":"J. Funct. Spaces Appl."},{"issue":"2","key":"9940_CR19","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(2), 109\u2013116 (2007)","journal-title":"Proc. A. Razmadze Math. Inst."},{"issue":"2","key":"9940_CR20","doi-asserted-by":"publisher","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. Iberoam. 20(2), 493\u2013515 (2004). https:\/\/doi.org\/10.4171\/RMI\/398","journal-title":"Rev. Mat. Iberoam."},{"issue":"2","key":"9940_CR21","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1007\/s00013-007-2035-4","volume":"89","author":"TS Kopaliani","year":"2007","unstructured":"Kopaliani, T.S.: Infimal convolution and Muckenhoupt $$A_{p(\\cdot )}$$ condition in variable $$L^p$$ spaces. Arch. Math. 89(2), 185\u2013192 (2007). https:\/\/doi.org\/10.1007\/s00013-007-2035-4","journal-title":"Arch. Math."},{"key":"9940_CR22","doi-asserted-by":"publisher","unstructured":"Koshelev, A.: Regularity Problem for Quasilinear Elliptic and Parabolic Systems, pp. 21\u2013255. Springer, Berlin (1995). https:\/\/doi.org\/10.1007\/BFb0094482","DOI":"10.1007\/BFb0094482"},{"key":"9940_CR23","first-page":"325","volume":"18","author":"S Leonardi","year":"1999","unstructured":"Leonardi, S.: Remarks on the regularity of solutions of elliptic systems. Appl. Nonlinear Anal. 18, 325\u2013344 (1999)","journal-title":"Appl. Nonlinear Anal."},{"issue":"1","key":"9940_CR24","first-page":"43","volume":"43","author":"S Leonardi","year":"2002","unstructured":"Leonardi, S.: Weighted Miranda-Talenti inequality and applications to equations with discontinuous coefficients. Commentat. Math. Univ. Carol. 43(1), 43\u201359 (2002)","journal-title":"Commentat. Math. Univ. Carol."},{"key":"9940_CR25","doi-asserted-by":"publisher","unstructured":"Ohno, T.: Continuity properties for logarithmic potentials of functions in Morrey spaces of variable exponent. Hiroshima Math. J. 38(3), 363\u2013383 (2008). https:\/\/doi.org\/10.32917\/hmj\/1233152775","DOI":"10.32917\/hmj\/1233152775"},{"issue":"3","key":"9940_CR26","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1007\/s43037-021-00128-8","volume":"15","author":"H Rafeiro","year":"2011","unstructured":"Rafeiro, H., Samko, S.: On embeddings of Morrey type spaces between weighted Lebesgue or Stummel spaces with application to Herz spaces. Banach J. Math. Anal. 15(3), 48 (2011). https:\/\/doi.org\/10.1007\/s43037-021-00128-8","journal-title":"Banach J. Math. Anal."},{"issue":"1","key":"9940_CR27","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1023\/A:1013749603910","volume":"51","author":"MA Ragusa","year":"2001","unstructured":"Ragusa, M.A., Zamboni, P.: A potential theoretic inequality. Czech. Math. J. 51(1), 55\u201365 (2001). https:\/\/doi.org\/10.1023\/A:1013749603910","journal-title":"Czech. Math. J."},{"issue":"1","key":"9940_CR28","doi-asserted-by":"publisher","first-page":"560","DOI":"10.1016\/j.jmaa.2007.01.091","volume":"335","author":"NG Samko","year":"2007","unstructured":"Samko, N.G., Samko, S.G., Vakulov, B.G.: Weighted Sobolev theorem in Lebesgue spaces with variable exponent. J. Math. Anal. Appl. 335(1), 560\u2013583 (2007). https:\/\/doi.org\/10.1016\/j.jmaa.2007.01.091","journal-title":"J. Math. Anal. Appl."},{"issue":"3","key":"9940_CR29","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1155\/2010\/659456","volume":"8","author":"N Samko","year":"2010","unstructured":"Samko, N., Samko, S., Vakulov, B.: Fractional integrals and hypersingular integrals in variable order H\u00f6lder spaces on homogeneous spaces. J. Funct. Spaces Appl. 8(3), 215\u2013244 (2010). https:\/\/doi.org\/10.1155\/2010\/659456","journal-title":"J. Funct. Spaces Appl."},{"issue":"2","key":"9940_CR30","doi-asserted-by":"publisher","first-page":"627","DOI":"10.7153\/mia-17-46","volume":"17","author":"S Samko","year":"2014","unstructured":"Samko, S.: Morrey spaces are closely embedded between vanishing Stummel spaces. Math. Inequal. Appl. 17(2), 627\u2013639 (2014). https:\/\/doi.org\/10.7153\/mia-17-46","journal-title":"Math. Inequal. Appl."},{"key":"9940_CR31","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1007\/BF01452327","volume":"132","author":"F Stummel","year":"1956","unstructured":"Stummel, F.: Singul\u00e4re elliptische Differentialoperatoren in Hilbertschen R\u00e4umen. Math. Ann. 132, 150\u2013176 (1956). https:\/\/doi.org\/10.1007\/BF01452327","journal-title":"Math. Ann."}],"updated-by":[{"DOI":"10.1007\/s00041-023-10033-3","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2023,8,17]],"date-time":"2023-08-17T00:00:00Z","timestamp":1692230400000}}],"container-title":["Journal of Fourier Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00041-022-09940-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00041-022-09940-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00041-022-09940-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,23]],"date-time":"2023-08-23T04:07:08Z","timestamp":1692763628000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00041-022-09940-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,18]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["9940"],"URL":"https:\/\/doi.org\/10.1007\/s00041-022-09940-8","relation":{},"ISSN":["1069-5869","1531-5851"],"issn-type":[{"value":"1069-5869","type":"print"},{"value":"1531-5851","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,18]]},"assertion":[{"value":"6 October 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 March 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 April 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 May 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 August 2023","order":5,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Correction","order":6,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"A Correction to this paper has been published:","order":7,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"https:\/\/doi.org\/10.1007\/s00041-023-10033-3","URL":"https:\/\/doi.org\/10.1007\/s00041-023-10033-3","order":8,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"50"}}