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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 bilinear fractional integral, $L^p$ spaces, Heat kernel
MSC Classifications: 43A22, 43A32, 43B25 show english descriptions Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
Other transforms and operators of Fourier type
unknown classification 43B25
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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