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arXiv · 2509.19584

One-sided Fractional Integrals and Riesz Potentials on a Spherical Cap

Boris Rubin
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Abstract

We introduce fractional integrals on the $n$-dimensional spherical cap, study their boundednes in weighted $L^p$ spaces and obtain explicit inversion formulas. The results are applied to the inversion problem for Riesz potentials on a spherical cap. In the case $n=2$, this problem arises in electrostatics, elasticity, and some other applied areas. The main tools are stereographic projection, hypersingular integrals of the Marchaud type, Poisson integrals, and spherical harmonic decompositions.

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Boris Rubin. 2025-09-23. One-sided Fractional Integrals and Riesz Potentials on a Spherical Cap. https://arxiv.org/abs/2509.19584

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