{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T13:44:59Z","timestamp":1775396699255,"version":"3.50.1"},"reference-count":0,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2000,1,1]],"date-time":"2000-01-01T00:00:00Z","timestamp":946684800000},"content-version":"vor","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":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Function Spaces"],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>In connection with application to various problems of operator\ntheory, we study almost monotonic functions <jats:italic>w<\/jats:italic>(<jats:italic>x, r<\/jats:italic>) depending on a parameter\n<jats:italic>x<\/jats:italic> which runs a metric measure space <jats:italic>X<\/jats:italic>, and the so called index numbers\n<jats:italic>m<\/jats:italic>(<jats:italic>w, x<\/jats:italic>), <jats:italic>M<\/jats:italic>(<jats:italic>w, x<\/jats:italic>) of such functions, and consider some generalized Zygmund,\nBary, Lozinskii and Stechkin conditions. The main results contain necessary\nand sufficient conditions, in terms of lower and upper bounds of indices <jats:italic>m<\/jats:italic>(<jats:italic>w, x<\/jats:italic>)\nand <jats:italic>M<\/jats:italic>(<jats:italic>w, x<\/jats:italic>) , for the uniform belongness of functions <jats:italic>w<\/jats:italic>(\u00b7, <jats:italic>r<\/jats:italic>) to Zygmund\u2010Bary\u2010Stechkin classes. We give also applications to local dimensions in metric measure spaces\nand characterization of some integral inequalities involving radial weights and\nmeasures of balls in such spaces.<\/jats:p>","DOI":"10.1155\/2009\/929041","type":"journal-article","created":{"date-parts":[[2011,12,26]],"date-time":"2011-12-26T11:36:41Z","timestamp":1324899401000},"page":"61-89","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces"],"prefix":"10.1155","volume":"7","author":[{"given":"Natasha","family":"Samko","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2009,1]]},"container-title":["Journal of Function Spaces"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jfs\/2009\/929041.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2009\/929041","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T02:58:31Z","timestamp":1723085911000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2009\/929041"}},"subtitle":[],"editor":[{"given":"Vladimir D.","family":"Stepanov","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1155\/2009\/929041"],"URL":"https:\/\/doi.org\/10.1155\/2009\/929041","archive":["Portico"],"relation":{},"ISSN":["2314-8896","2314-8888"],"issn-type":[{"value":"2314-8896","type":"print"},{"value":"2314-8888","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]},"assertion":[{"value":"2007-12-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2009-01-01","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}