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March, 2005 Rough Singular Integrals with Kernels Supported by Submanifolds of Finite Type
Hussain Al-Qassem, Ahmad Al-Salman, Yibiao Pan
Asian J. Math. 9(1): 019-030 (March, 2005).

Abstract

Our point of departure is the following $L^{p}$ boundedness result form [St], Theorem 1.1, ... Recently, the results in Theorem 1.1 were improved by Fan, Guo, and Pan in [FGP] who showed that the $L^{p}$ boundedness of $T_{\Phi}$ and $M_{\Phi}$ continues to hold if the condition $\Omega \in \mathbb{C}^{1}(Sn-1)$ is replaced by the weaker condition $\Omega \in L^{q}(Sn-1)$ for some $q > 1$. Also, the authors of [FGP] were able to establish the $L^{p}$ boundedness of the maximal operator $T^{*}_{\Phi}$ under the condition $\Omega \in L^{q}(Sn-1)$ for some $q > 1$. The main purpose of this paper is to present further improvements of the above results in which the condition $\Omega \in L^{q}(Sn-1)$ is replaced by a weaker condition $\Omega \in B^{0,0}_{q}(Sn-1)$ ...

Citation

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Hussain Al-Qassem. Ahmad Al-Salman. Yibiao Pan. "Rough Singular Integrals with Kernels Supported by Submanifolds of Finite Type." Asian J. Math. 9 (1) 019 - 030, March, 2005.

Information

Published: March, 2005
First available in Project Euclid: 13 June 2005

zbMATH: 1104.42006
MathSciNet: MR2150688

Rights: Copyright © 2005 International Press of Boston

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Vol.9 • No. 1 • March, 2005
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