{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,30]],"date-time":"2025-06-30T21:21:35Z","timestamp":1751318495338,"version":"3.37.3"},"reference-count":34,"publisher":"Wiley","license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["SFRH\/BPD\/34258\/2006"],"award-info":[{"award-number":["SFRH\/BPD\/34258\/2006"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Function Spaces and Applications"],"published-print":{"date-parts":[[2012]]},"abstract":"<jats:p>We study the weighted<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>p<\/mml:mi><mml:mo>\u2192<\/mml:mo><mml:mi>q<\/mml:mi><\/mml:math>-boundedness of Hardy-type operators in Morrey spaces<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:msup><mml:mrow><mml:mi>\u2112<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>p<\/mml:mi><mml:mo>,<\/mml:mo><mml:mo>\u03bb<\/mml:mo><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>(<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:msup><mml:mrow><mml:mi>\u211d<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>) (or<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:msup><mml:mrow><mml:mi>\u2112<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>p<\/mml:mi><mml:mo>,<\/mml:mo><mml:mo>\u03bb<\/mml:mo><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>(<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>\u211d<\/mml:mi><\/mml:mrow><mml:mrow><mml:mo>+<\/mml:mo><\/mml:mrow><mml:mrow><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msubsup><\/mml:mrow><\/mml:math>) in the one-dimensional case) for a class of almost monotonic weights. The obtained results are applied to a similar weighted<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mi>p<\/mml:mi><mml:mo>\u2192<\/mml:mo><mml:mi>q<\/mml:mi><\/mml:math>-boundedness of the Riesz potential operator. The conditions on weights, both for the Hardy and potential operators, are necessary and sufficient in the case of power weights. In the case of more general weights, we provide separately necessary and sufficient conditions in terms of Matuszewska-Orlicz indices of weights.<\/jats:p>","DOI":"10.1155\/2012\/678171","type":"journal-article","created":{"date-parts":[[2012,2,9]],"date-time":"2012-02-09T16:03:32Z","timestamp":1328803412000},"page":"1-21","source":"Crossref","is-referenced-by-count":20,"title":["Weighted Hardy and Potential Operators in Morrey Spaces"],"prefix":"10.1155","volume":"2012","author":[{"given":"Natasha","family":"Samko","sequence":"first","affiliation":[{"name":"Department of Mathematics, Research Center CEAF, Instituto Superior T\u00e9cnico, 1049-003 Lisbon, Portugal"}]}],"member":"311","reference":[{"key":"21","doi-asserted-by":"publisher","DOI":"10.2307\/1989904"},{"volume":"105","year":"1983","key":"12"},{"year":"1977","key":"16"},{"volume":"81","year":"2000","series-title":"Mathematical Surveys and Monographs","key":"37"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-75-04265-9"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.2004.53.2470"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.2307\/2044236"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1002\/mana.3211850102"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2006.10.085"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.4064\/sm163-2-4"},{"issue":"3-4","key":"9","first-page":"273","volume":"7","year":"1987","journal-title":"Rendiconti di Matematica"},{"issue":"5","key":"10","first-page":"323","volume":"7","year":"1991","journal-title":"Bollettino dell'Unione Matematica Italiana"},{"key":"11","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1017\/S0027763000025411","volume":"167","year":"2002","journal-title":"Nagoya Mathematical Journal"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1002\/mana.19941660108"},{"issue":"3","key":"23","doi-asserted-by":"crossref","first-page":"587","DOI":"10.11650\/twjm\/1500574952","volume":"5","year":"2001","journal-title":"Taiwanese Journal of Mathematics"},{"issue":"3","key":"24","first-page":"463","volume":"54","year":"2001","journal-title":"Scientiae Mathematicae Japonicae"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1023\/B:POTA.0000010664.71807.f6"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1007\/BF02414340"},{"key":"27","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/0022-1236(69)90022-6","volume":"4","year":"1969","journal-title":"Journal of Functional Analysis"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-007-9176-7"},{"issue":"3","key":"33","doi-asserted-by":"crossref","first-page":"683","DOI":"10.14492\/hokmj\/1285766424","volume":"35","year":"2006","journal-title":"Hokkaido Mathematical Journal"},{"key":"34","first-page":"593","volume":"19","year":"1965","journal-title":"Annali della Scuola Normale Superiore di Pisa"},{"issue":"19","key":"35","first-page":"443","volume":"3","year":"1965","journal-title":"Annali della Scuola Normale Superiore di Pisa"},{"key":"32","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2008.09.021"},{"key":"5","first-page":"483","volume":"5","year":"1956","journal-title":"Proceedings of the Moscow Mathematical Society"},{"issue":"4","key":"13","first-page":"437","volume":"7","year":"2004","journal-title":"Fractional Calculus & Applied Analysis"},{"year":"1978","key":"15"},{"volume":"234, article 49","journal-title":"Dissertationes Mathematicae","year":"1985","key":"18"},{"volume":"5","year":"1989","key":"19"},{"key":"20","doi-asserted-by":"crossref","first-page":"11","DOI":"10.4064\/sm-26-1-11-24","volume":"26","year":"1965","journal-title":"Studia Mathematica"},{"key":"30","first-page":"107","volume":"120","year":"1999","journal-title":"Proceedings of A. 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