Abstract
We investigate the properties of spaces with generalized smoothness, such as Calderón 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. The kernels of potentials may have non-power singularities at the origin. Using order-sharp estimates for the moduli of continuity of potentials, we establish criteria for the embeddings of potentials into Calderón spaces and describe the optimal spaces for such embeddings.
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Funding
The work of E. G. Bakhtigareeva and M. L. Goldman is supported by the Russian Science Foundation under grant 19-11-00087 and performed in Steklov Mathematical Institute of Russian Academy of Sciences.
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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Vol. 312, pp. 43–81 https://doi.org/10.4213/tm4141.
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Bakhtigareeva, E.G., Goldman, M.L. & Haroske, D.D. Optimal Calderón Spaces for Generalized Bessel Potentials. Proc. Steklov Inst. Math. 312, 37–75 (2021). https://doi.org/10.1134/S008154382101003X
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DOI: https://doi.org/10.1134/S008154382101003X