{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T07:13:20Z","timestamp":1776323600220,"version":"3.50.1"},"reference-count":44,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100006252","name":"Lule\u00e5 University of Technology","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100006252","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Function Spaces and Applications"],"published-print":{"date-parts":[[2013]]},"abstract":"We study thep<\/mml:mi>\u00b7<\/mml:mo><\/mml:mrow><\/mml:mfenced>\u2192<\/mml:mo>q<\/mml:mi>\u00b7<\/mml:mo><\/mml:mrow><\/mml:mfenced><\/mml:math>boundedness of weighted multidimensional Hardy-type operatorsH<\/mml:mi><\/mml:mrow>w<\/mml:mi><\/mml:mrow>\u03b1<\/mml:mi>\u00b7<\/mml:mo><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:msubsup><\/mml:mrow><\/mml:math>and\u210b<\/mml:mi><\/mml:mrow>w<\/mml:mi><\/mml:mrow>\u03b1<\/mml:mi>\u00b7<\/mml:mo><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:msubsup><\/mml:mrow><\/mml:math>of variable order\u03b1<\/mml:mi>x<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:math>, with radial weightw<\/mml:mi>x<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:mfenced><\/mml:math>, from a variable exponent locally generalized Morrey space\u2112<\/mml:mi><\/mml:mrow>p<\/mml:mi>\u00b7<\/mml:mo><\/mml:mrow><\/mml:mfenced>,<\/mml:mo>\u03c6<\/mml:mi>\u00b7<\/mml:mo><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:msup>\u211d<\/mml:mi><\/mml:mrow>n<\/mml:mi><\/mml:mrow><\/mml:msup>,<\/mml:mo>w<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:math>to another\u2112<\/mml:mi><\/mml:mrow>q<\/mml:mi>\u00b7<\/mml:mo><\/mml:mrow><\/mml:mfenced>,<\/mml:mo>\u03c8<\/mml:mi>\u00b7<\/mml:mo><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:msup>\u211d<\/mml:mi><\/mml:mrow>n<\/mml:mi><\/mml:mrow><\/mml:msup>,<\/mml:mo>w<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:math>. The exponents are assumed to satisfy the decay condition at the origin and infinity. We construct certain functions, defined byp<\/mml:mi><\/mml:mrow><\/mml:math>,\u03b1<\/mml:mi><\/mml:mrow><\/mml:math>, and\u03c6<\/mml:mi><\/mml:mrow><\/mml:math>, the belongness of which to the resulting space\u2112<\/mml:mi><\/mml:mrow>q<\/mml:mi>\u00b7<\/mml:mo><\/mml:mrow><\/mml:mfenced>,<\/mml:mo>\u03c8<\/mml:mi>\u00b7<\/mml:mo><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:msup>\u211d<\/mml:mi><\/mml:mrow>n<\/mml:mi><\/mml:mrow><\/mml:msup>,<\/mml:mo>w<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:math>is sufficient for such a boundedness. Under additional assumptions on\u03c6<\/mml:mi>\/<\/mml:mo>w<\/mml:mi><\/mml:math>, this condition is also necessary. We also give the boundedness conditions in terms of Zygmund-type integral inequalities for the functions\u03c6<\/mml:mi><\/mml:mrow><\/mml:math>and\u03c6<\/mml:mi>\/<\/mml:mo>w<\/mml:mi><\/mml:math>.<\/jats:p>","DOI":"10.1155\/2013\/716029","type":"journal-article","created":{"date-parts":[[2013,11,1]],"date-time":"2013-11-01T03:10:02Z","timestamp":1383275402000},"page":"1-11","source":"Crossref","is-referenced-by-count":9,"title":["Weighted Hardy-Type Inequalities in Variable Exponent Morrey-Type Spaces"],"prefix":"10.1155","volume":"2013","author":[{"given":"Dag","family":"Lukkassen","sequence":"first","affiliation":[{"name":"Narvik University College and Norut Narvik, P.O. Box 385, N-8505 Narvik, Norway"}]},{"given":"Lars-Erik","family":"Persson","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Lule\u00e5 University of Technology, SE 971 87 Lule\u00e5, Sweden"},{"name":"Narvik University College, P.O. Box 385, N-8505, Narvik, Norway"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8022-2863","authenticated-orcid":true,"given":"Stefan","family":"Samko","sequence":"additional","affiliation":[{"name":"Universidade do Algarve, FCT, Campus de Gambelas, Faro 8005-139, Portugal"}]},{"given":"Peter","family":"Wall","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Lule\u00e5 University of Technology, SE 971 87 Lule\u00e5, Sweden"}]}],"member":"311","reference":[{"key":"8","year":"2013"},{"key":"10","series-title":"Lecture Notes in Mathematics","volume":"2017","year":"2011"},{"key":"35","series-title":"Lecture Notes in Mathematics","volume":"1748","year":"2000"},{"key":"27","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1090\/S0002-9947-1938-1501936-8","volume":"43","year":"1938","journal-title":"American Mathematical Society"},{"key":"12","year":"1983"},{"key":"23","year":"1977"},{"key":"44","series-title":"Mathematical Surveys and 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