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arXiv · 2505.11851

On the Boundedness of Hypersingular Integrals Along Certain Radial Hypersurfaces

Sajin Vincent A W·Aniruddha Deshmukh·Vijay Kumar Sohani
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Abstract

We study a class of oscillatory hypersingular integral operators associated to a radial hypersurface of the form $\Gamma(t)=(t,\varphi(t)), t\in\R{n}$. When $\varphi$ satisfies suitable curvature and monotonicity conditions, we prove $L^p(\R{{n+1}})$ boundedness of the operator, where the range of $p$ depends on the hypersingularity of the operator. We also establish certain Sobolev estimates of the operator under consideration.

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Sajin Vincent A W, Aniruddha Deshmukh, Vijay Kumar Sohani. 2025-05-17. On the Boundedness of Hypersingular Integrals Along Certain Radial Hypersurfaces. https://arxiv.org/abs/2505.11851

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