Estimates for continuity envelopes and approximation numbers of Bessel potentials

In this paper we study spaces of Bessel potentials in n-dimensional Euclidean spaces. They are constructed on the basis of a rearrangement-invariant space (RIS) by using convolutions with Bessel-MacDonald kernels. Specifically, the treatment covers spaces of classical Bessel potentials. We establish two-sided estimates for the corresponding modulus of smoothness of order k∈N, ωk (f ; t), and determine their continuity envelope functions. This result is then applied to estimate the approximation numbers of some embeddings. © 2013 Elsevier Inc.

Authors
Language
English
Pages
58-85
Status
Published
Volume
172
Year
2013
Organizations
  • 1 Peoples Friendship University of Russia, Department of Mathematical Analysis and Function Theory, Miklukho Maklai 6, Moscow 117198, Russian Federation
  • 2 Mathematical Institute, Friedrich-Schiller-University Jena, D-07737 Jena, Germany
Keywords
Approximation numbers; Compact embeddings; Continuity envelopes; Convolution; Rearrangement invariant space; Space of potentials
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Zubkov F.I., Zaytsev V.P., Obushak M.D., Ershova Y.D., Mertsalov D.F., Sorokina E.A., Nikitina E.V., Gorak Y.I., Lytvyn R.Z., Varlamov A.V.
Chemistry of Heterocyclic Compounds. Латвийский институт органического синтеза Латвийской академии наук / Springer New York Consultants Bureau. Vol. 49. 2013. P. 746-759