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# A Bilinear Fractional Integral on Compact Lie Groups

Published:2010-08-26
Printed: Jun 2011
• Jiecheng Chen,
Department of Mathematics, Zhejiang University, Hangzhou, China
• Dashan Fan,
Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI 53217, U.S.A.
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## Abstract

As an analog of a well-known theorem on the bilinear fractional integral on $\mathbb{R}^{n}$ by Kenig and Stein, we establish the similar boundedness property for a bilinear fractional integral on a compact Lie group. Our result is also a generalization of our recent theorem about the bilinear fractional integral on torus.
 Keywords: bilinear fractional integral, $L^p$ spaces, Heat kernel
 MSC Classifications: 43A22 - Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 43A32 - Other transforms and operators of Fourier type 43B25 - unknown classification 43B25

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