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arXiv · 2307.08977

On Sharpness of $L\log L$ Criterion for Weak Type $(1,1)$ boundedness of rough operators

Ankit Bhojak
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Abstract

In this note, we show that the $L\log L$ hypothesis is the strongest size condition on a homogeneous rough function on the sphere which ensures the weak type $(1,1)$ boundedness of the corresponding singular integral $T_\Omega$, provided $T_\Omega$ is bounded in $L^2$.

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BibTeXRIS

Ankit Bhojak. 2023-07-18. On Sharpness of $L\log L$ Criterion for Weak Type $(1,1)$ boundedness of rough operators. https://arxiv.org/abs/2307.08977

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