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Search: MSC category 43A32 ( Other transforms and operators of Fourier type )

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1. CMB Online first

Koh, Doowon
Restriction Operators Acting on Radial Functions on Vector Spaces Over Finite Fields
We study $L^p-L^r$ restriction estimates for algebraic varieties $V$ in the case when restriction operators act on radial functions in the finite field setting. We show that if the varieties $V$ lie in odd dimensional vector spaces over finite fields, then the conjectured restriction estimates are possible for all radial test functions. In addition, assuming that the varieties $V$ are defined in even dimensional spaces and have few intersection points with the sphere of zero radius, we also obtain the conjectured exponents for all radial test functions.

Keywords:finite fields, radial functions, restriction operators
Categories:42B05, 43A32, 43A15

2. CMB 2010 (vol 54 pp. 207)

Chen, Jiecheng; Fan, Dashan
A Bilinear Fractional Integral on Compact Lie Groups
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
Categories:43A22, 43A32, 43B25

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