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February 2006 Singular and fractional integrals along variable surfaces
Dashan FAN, Shuichi SATO
Hokkaido Math. J. 35(1): 61-85 (February 2006). DOI: 10.14492/hokmj/1285766308

Abstract

We study singular integrals associated with the variable surfaces of revolution. We treat the rough kernel case where the singular integral is defined by an $H^1$ kernel function on the sphere $S^{n-1}$. We prove the $L^p$ boundedness of the singular integral for $1<p\leq 2$ assuming that a certain lower dimensional maximal operator is bounded on $L^s$ for all $s>1$. We also study the $(L^p,L^r)$ boundedness for fractional integrals associated with surfaces of revolution.

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Dashan FAN. Shuichi SATO. "Singular and fractional integrals along variable surfaces." Hokkaido Math. J. 35 (1) 61 - 85, February 2006. https://doi.org/10.14492/hokmj/1285766308

Information

Published: February 2006
First available in Project Euclid: 29 September 2010

zbMATH: 1129.42354
MathSciNet: MR2225082
Digital Object Identifier: 10.14492/hokmj/1285766308

Subjects:
Primary: 42B20

Keywords: fractional integral , Hardy space , Rough kernel , singular integral

Rights: Copyright © 2006 Hokkaido University, Department of Mathematics

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Vol.35 • No. 1 • February 2006
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