Linear and nonlinear Bessel potentials associated with the Poly-axially operator

Abstract

ABSTRACT In this work, we will study a Bessel potential spaces , () associated with the Poly-axially operator and their properties. We define the Sobolev-type spaces ) and we prove an analogue of Calderón's theorem for Fourier–Bessel transform. We define the nonlinear Bessel potentials associated with a measure ν and the -capacity. Finally, we establish a classical problem of existence of an extremal function for the -capacity.