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arXiv · 2202.13584

Fractional integration with singularity on the light-cone

Zipeng Wang
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Abstract

We study a family of convolution operators whose symbols and kernels have singularity on the light-cone in $\mathbb{R}^{n+1}$. First, we prove a desired ${\bf L}^p\to {\bf L}^q$ norm inequality which has been left open. Moreover, we obtain certain sharp regularity results for the cone multiplier problem of negative order.

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Zipeng Wang. 2022-02-28. Fractional integration with singularity on the light-cone. https://doi.org/10.13140/rg.2.2.28849.86885

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