On the Boundedness of Hypersingular Integrals Along Certain Radial Hypersurfaces

2025/05/17 by Wei Sha, W, Sajin Vincent A, Aniruddha Deshmukh +3
Mathematics · #42B15 #42B20 #47A30 #47B38 #Advanced Harmonic Analysis Research #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2505.11851

openalex publication_date 2025/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a class of oscillatory hypersingular integral operators associated to a radial hypersurface of the form Γ(t)=(t,φ(t)), t∈\Rn. When φ satisfies suitable curvature and monotonicity conditions, we prove L^p(\Rn+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.

Related

• A type of oscillatory integral operator and its applications
• Damped oscillatory integrals and boundedness of maximal operators associated to mixed homogeneous hypersurfaces
• On Polynomial Carleson operators along quadratic hypersurfaces
• On multilinear oscillatory integrals, nonsingular and singular
• L²-estimates for singular oscillatory integral operators