Modulus of Continuity for Bessel Type Potential over Lorentz Space

Abstract

The generalized Bessel potentials are constructed using convolutions of the generalized Bessel–McDonald kernels with functions belonging to a basic rearrangement invariant space. Under assumptions ensuring the embedding of potentials into the space of bounded continuous functions, differential properties of potentials are described by using the k-th order modulus of continuity in the uniform norm. In the paper, estimates are given for the k-th order modulus of continuity in the uniform norm in the case of the generalized Bessel potentials constructed over the basic weighted Lorentz space.