Modulus of continuity for Bessel type poteniial over Lorentz space

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.