Optimal calderon space for bessel potentials

Abstract

The paper is devoted to Bessel potentials constructed by convolutions of Bessel–McDonald kernelswith functions from the basic rearrangement invariantspace. If the criterion is fulfilled for the embedding ofpotentials into the space of bounded continuous functions, we state the equivalent description for the conesof moduli of continuity of potentials in the uniformnorm. This makes it possible to obtain the criterion forthe embedding of potentials into the Calderon space.In the case of Bessel potentials constructed over thebasic weighted Lorentz space, we explicitly describethe optimal Calderon space for such an embedding.1. DESCRIPTION OF THE CONE OF CONTINUITY MODULI FOR POTENTIALSLet