3 papers
math.FA2025
One-sided Fractional Integrals and Riesz Potentials on a Spherical Cap
Boris Rubin
We introduce fractional integrals on the -dimensional spherical cap, study their boundednes in weighted spaces and obtain explicit inversion formulas. The results are appl…
math.FA2024
Fractional Integrals and Tangency Problems in Integral Geometry
Boris Rubin
Many known Radon-type transforms of symmetric (radial or zonal) functions are represented by one-dimensional Riemann-Liouville fractional integrals or their modifications. The pres…
math.FA2021
Higher-Rank Radon Transforms on Constant Curvature Spaces
Boris Rubin
We study higher-rank Radon transforms that take functions on -dimensional totally geodesic submanifolds in the -dimensional real constant curvature space to functions on simi…