Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions

Abstract

We apply a symmetrization procedure to the setting of Jacobi expansions and study potential spaces in the resulting situation. We prove that the potential spaces of integer orders are isomorphic to suitably defined Sobolev spaces. Among further results, we obtain a fractional square function characterization, structural theorems and Sobolev type embedding theorems for these potential spaces.

References in corpus (2)

• Riesz-Jacobi transforms as principal value integrals
• Variable exponent Sobolev spaces associated with Jacobi expansions

Cited by in corpus (2)

• On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings
• On derivatives, Riesz transforms and Sobolev spaces for Fourier-Bessel expansions