Estimates for Continuity Envelopes and Approximation Numbers of Generalized Bessel Potentials over Lorentz Space

Abstract

In this paper we study spaces of Bessel potentials in n-dimensional Euclidean spaces. They are constructed on the basis of a rearrangement-invariant space (RIS) by using convolutions with Bessel– MacDonald kernels. The differential properties of potentials are characterized by their modulus of continuity of order  in the uniform norm.  Specifically, the treatment covers spaces of Generalized Bessel potentials constructed over the basic weighted Lorentz space. In particular, we determine continuity envelope function. This result is then applied to estimate the approximation numbers of Generalized Bessel potentials when Generalized Bessel potentials constructed over the basic weighted Lorentz space.