{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T11:02:24Z","timestamp":1772449344075,"version":"3.50.1"},"reference-count":40,"publisher":"Wiley","issue":"9-10","license":[{"start":{"date-parts":[[2007,6,18]],"date-time":"2007-06-18T00:00:00Z","timestamp":1182124800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematische Nachrichten"],"published-print":{"date-parts":[[2007,7]]},"abstract":"Abstract<\/jats:title>We study the boundedness of singular Calder\u00f3n\u2013Zygmund type operators in the spacesL<\/jats:italic>p<\/jats:italic>(\u00b7)<\/jats:sup>(\u03a9,\u03c1<\/jats:italic>) over a bounded open set in \u211dn<\/jats:italic><\/jats:sup>with the weight\u03c1<\/jats:italic>(x<\/jats:italic>) =$ \\prod ^m_{k=1} $<\/jats:styled-content>w<\/jats:italic>k<\/jats:italic><\/jats:sub>(|x<\/jats:italic>\u2013x<\/jats:italic>k<\/jats:italic><\/jats:sub>|),x<\/jats:italic>k<\/jats:italic><\/jats:sub>\u2208$ \\bar \\Omega $<\/jats:styled-content>, wherew<\/jats:italic>k<\/jats:italic><\/jats:sub>has the property that$ r^{ {n \\over {p(x_k)}} } $<\/jats:styled-content>w<\/jats:italic>k<\/jats:italic><\/jats:sub>(r<\/jats:italic>) \u2208$ \\Phi ^0_n $<\/jats:styled-content>, where$ \\Phi ^0_n $<\/jats:styled-content>is a certain Zygmund\u2010type class. The boundedness of the singular Cauchy integral operatorS<\/jats:italic>\u0393<\/jats:sub>along a Carleson curve \u0393 is also considered in the spacesL<\/jats:italic>p<\/jats:italic>(\u00b7)<\/jats:sup>(\u0393,\u03c1<\/jats:italic>) with similar weights.<\/jats:p>The weight functionsw<\/jats:italic>k<\/jats:italic><\/jats:sub>may oscillate between two power functions with different exponents. It is assumed that the exponentp<\/jats:italic>(\u00b7) satisfies the Dini\u2013Lipschitz condition. The final statement on the boundedness is given in terms of the index numbers of the functionswk<\/jats:italic>(similar in a sense to the Boyd indices for the Young functions defining Orlicz spaces). (\u00a9 2007 WILEY\u2010VCH Verlag GmbH & Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/mana.200510542","type":"journal-article","created":{"date-parts":[[2007,6,18]],"date-time":"2007-06-18T16:49:02Z","timestamp":1182185342000},"page":"1145-1156","source":"Crossref","is-referenced-by-count":21,"title":["Singular operators in variable spacesL<\/i>p<\/i>(\u00b7)<\/sup>(\u03a9,\u03c1<\/i>) with oscillating weights"],"prefix":"10.1002","volume":"280","author":[{"given":"Vakhtang","family":"Kokilashvili","sequence":"first","affiliation":[]},{"given":"Natasha","family":"Samko","sequence":"additional","affiliation":[]},{"given":"Stefan","family":"Samko","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2007,6,18]]},"reference":[{"issue":"1","key":"e_1_2_1_2_2","first-page":"123","article-title":"Estimates with A\u221e weights for various singular integral operators","volume":"8","author":"Alvarez T.","year":"1994","journal-title":"Boll. Un. Mat. 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