Optimal Calder\'on Spaces for generalized Bessel potentials
Functional Analysis
2020-07-17 v1
Abstract
In the paper we investigate the properties of spaces with generalized smoothness, such as Calder\'on spaces that include the classical Nikolskii-Besov spaces and many of their generalizations, and describe differential properties of generalized Bessel potentials that include classical Bessel potentials and Sobolev spaces. Kernels of potentials may have non-power singularity at the origin. With the help of order-sharp estimates for moduli of continuity of potentials, we establish the criteria of embeddings of potentials into Calder\'on spaces, and describe the optimal spaces for such embeddings.
Cite
@article{arxiv.2007.08286,
title = {Optimal Calder\'on Spaces for generalized Bessel potentials},
author = {Elza Bakhtigareeva and Mikhail L. Goldman and Dorothee D. Haroske},
journal= {arXiv preprint arXiv:2007.08286},
year = {2020}
}