{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T06:22:39Z","timestamp":1774592559903,"version":"3.50.1"},"reference-count":42,"publisher":"Wiley","issue":"2-3","license":[{"start":{"date-parts":[[2011,1,3]],"date-time":"2011-01-03T00:00:00Z","timestamp":1294012800000},"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":[[2011,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider non\u2010standard generalized H\u00f6lder spaces of functions<jats:italic>f<\/jats:italic>on the unit sphere<jats:styled-content>\\documentclass{article}\\usepackage{amssymb}\\pagestyle{empty}\\begin{document}${\\mathbb S}^{n-1} $\\end{document}<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-ueqn-1.gif\" xlink:title=\"equation image\"\/><\/jats:styled-content>in<jats:styled-content>\\documentclass{article}\\usepackage{amssymb}\\pagestyle{empty}\\begin{document}${\\mathbb R}^n $\\end{document}<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-ueqn-2.gif\" xlink:title=\"equation image\"\/><\/jats:styled-content>, whose local continuity modulus \u03a9(<jats:italic>f<\/jats:italic>,<jats:italic>x<\/jats:italic>,<jats:italic>h<\/jats:italic>) at a point<jats:styled-content>\\documentclass{article}\\usepackage{amssymb}\\pagestyle{empty}\\begin{document}$x\\in {\\mathbb S}^{n-1} $\\end{document}<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-ueqn-3.gif\" xlink:title=\"equation image\"\/><\/jats:styled-content>has a dominant \u03c9(<jats:italic>x<\/jats:italic>,<jats:italic>h<\/jats:italic>) which may vary from point to point. We establish theorems on the mapping properties of spherical potential operators of variable order \u03b1(<jats:italic>x<\/jats:italic>), from such a variable generalized H\u00f6lder space to another one with a \u201cbetter\u201d dominant \u03c9<jats:sub>\u03b1<\/jats:sub>(<jats:italic>x<\/jats:italic>,<jats:italic>h<\/jats:italic>) =<jats:italic>h<\/jats:italic><jats:sup>\u211c\u03b1(<jats:italic>x<\/jats:italic>)<\/jats:sup>\u03c9(<jats:italic>x<\/jats:italic>,<jats:italic>h<\/jats:italic>), and similar mapping properties of spherical hypersingular integrals of variable order \u03b1(<jats:italic>x<\/jats:italic>) from such a space into the space with \u201cworse\u201d dominant \u03c9<jats:sub>\u2212\u03b1<\/jats:sub>(<jats:italic>x<\/jats:italic>,<jats:italic>h<\/jats:italic>) =<jats:italic>h<\/jats:italic><jats:sup>\u2212\u211c\u03b1(<jats:italic>x<\/jats:italic>)<\/jats:sup>\u03c9(<jats:italic>x<\/jats:italic>,<jats:italic>h<\/jats:italic>). We admit variable complex valued orders \u03b1(<jats:italic>x<\/jats:italic>) which may vanish at a set of measure zero. To cover this case, we consider the action of potential operators to weighted generalized H\u00f6lder spaces with the weight \u03b1(<jats:italic>x<\/jats:italic>). \u00a9 2011 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim<\/jats:p>","DOI":"10.1002\/mana.200810113","type":"journal-article","created":{"date-parts":[[2011,1,3]],"date-time":"2011-01-03T13:59:37Z","timestamp":1294063177000},"page":"355-369","source":"Crossref","is-referenced-by-count":17,"title":["Spherical fractional and hypersingular integrals of variable order in generalized H\u00f6lder spaces with variable characteristic"],"prefix":"10.1002","volume":"284","author":[{"given":"Natasha","family":"Samko","sequence":"first","affiliation":[]},{"given":"Boris","family":"Vakulov","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2011,1,3]]},"reference":[{"key":"e_1_2_4_2_2","first-page":"483","article-title":"Best approximations and differential properties of two conjugate functions (in Russian)","volume":"5","author":"Bary N. K.","year":"1956","journal-title":"Proc. Moscow Math. 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