On the Boundedness of Hypersingular Integrals Along Certain Radial Hypersurfaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913844480180224 |
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| author | W, Sajin Vincent A Deshmukh, Aniruddha Sohani, Vijay Kumar |
| author_facet | W, Sajin Vincent A Deshmukh, Aniruddha Sohani, Vijay Kumar |
| contents | We study a class of oscillatory hypersingular integral operators associated to a radial hypersurface of the form $Γ(t)=(t,φ(t)), t\in\R{n}$. When $φ$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_11851 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Boundedness of Hypersingular Integrals Along Certain Radial Hypersurfaces W, Sajin Vincent A Deshmukh, Aniruddha Sohani, Vijay Kumar Functional Analysis 42B20, 47A30, 42B15, 47B38 We study a class of oscillatory hypersingular integral operators associated to a radial hypersurface of the form $Γ(t)=(t,φ(t)), t\in\R{n}$. When $φ$ 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. |
| title | On the Boundedness of Hypersingular Integrals Along Certain Radial Hypersurfaces |
| topic | Functional Analysis 42B20, 47A30, 42B15, 47B38 |
| url | https://arxiv.org/abs/2505.11851 |