, 2012:179,
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Date: 23 Aug 2012

Weighted Trudinger inequality associated with rough multilinear fractional type operators

Abstract

Let http://static-content.springer.com/image/art%3A10.1186%2F1029-242X-2012-179/MediaObjects/13660_2012_302_IEq1_HTML.gif be the multilinear fractional type operator defined by http://static-content.springer.com/image/art%3A10.1186%2F1029-242X-2012-179/MediaObjects/13660_2012_302_IEq2_HTML.gif . In this paper, we study the weighted estimates for the Trudinger inequality associated to http://static-content.springer.com/image/art%3A10.1186%2F1029-242X-2012-179/MediaObjects/13660_2012_302_IEq1_HTML.gif with rough homogeneous kernels, which improve some known results significantly. A similar Trudinger inequality holds for another type of fractional integral defined by http://static-content.springer.com/image/art%3A10.1186%2F1029-242X-2012-179/MediaObjects/13660_2012_302_IEq3_HTML.gif , where http://static-content.springer.com/image/art%3A10.1186%2F1029-242X-2012-179/MediaObjects/13660_2012_302_IEq4_HTML.gif .