$L^p$ bounds for singular integrals and maximal singular integrals with rough kernels

Loukas Grafakos; Atanas Stefanov

$L^p$ bounds for singular integrals and maximal singular integrals with rough kernels

泛函分析 2016-09-07 v1

作者: Loukas Grafakos , Atanas Stefanov

摘要

Convolution type Calder\'on-Zygmund singular integral operators with rough kernels $\pv \Om(x)/|x|^n$ are studied. A condition on $\Om$ implying that the corresponding singular integrals and maximal singular integrals map $L^p \to L^p$ for $1<p<\nf$ is obtained. This condition is shown to be different from the condition $\Om\in H^1(\sn)$ .

关键词

operator theory and elliptic operators maximal operators lp spaces and inequalities

引用

@article{arxiv.math/9710205,
  title  = {$L^p$ bounds for singular integrals and maximal singular integrals with rough kernels},
  author = {Loukas Grafakos and Atanas Stefanov},
  journal= {arXiv preprint arXiv:math/9710205},
  year   = {2016}
}

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