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arXiv · 2007.08286

Optimal Calder\'on Spaces for generalized Bessel potentials

Elza Bakhtigareeva·Mikhail L. Goldman·Dorothee D. Haroske
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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.

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Elza Bakhtigareeva, Mikhail L. Goldman, Dorothee D. Haroske. 2020-07-16. Optimal Calder\'on Spaces for generalized Bessel potentials. https://arxiv.org/abs/2007.08286

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