Singular Integrals Associated to Hypersurfaces: $L^2$ Theory

Stephen Wainger; James Wright; Sarah Ziesler

Singular Integrals Associated to Hypersurfaces: $L^2$ Theory

泛函分析 2016-09-07 v1

作者: Stephen Wainger , James Wright , Sarah Ziesler

摘要

We consider singular integrals associated to a classical Calder\'on-Zygmund kernel $K$ and a hypersurface given by the graph of $\varphi(\psi(t))$ where $\varphi$ is an arbitrary $C^1$ function and $\psi$ is a smooth convex function of finite type. We give a characterization of those Calder\'on-Zygmund kernels $K$ and convex functions $\psi$ so that the associated singular integral operator is bounded on $L^2$ for all $C^1$ functions $\varphi$ .

关键词

singularity theory reproducing kernel hilbert space hypersurfaces

引用

@article{arxiv.math/9711212,
  title  = {Singular Integrals Associated to Hypersurfaces: $L^2$ Theory},
  author = {Stephen Wainger and James Wright and Sarah Ziesler},
  journal= {arXiv preprint arXiv:math/9711212},
  year   = {2016}
}

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