Some Generalized Besov-Type Space  with the Haar Basis

Some Generalized Besov-Type Space  with the Haar Basis

We introduce the generalized Besov-type space over the Haar basis. We give the two-sided estimate for the norm of functions of the space in terms of their Fourier–Haar coefficients. Also, we establish a criterion for the embedding and some two-sided estimate for the approximation of in the metric of...

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Bibliographic Details
Published in:Siberian mathematical journal Vol. 63; no. 6; pp. 1140 - 1152
Main Author: Smailov, E. S.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 2022
Springer Nature B.V
Subjects:
Mathematics
Mathematics and Statistics
approximation
Fourier–Haar coefficients
best approximation
embedding theorem
517.521.2
Besov space
Fourier–Haar series
Online Access:Get full text
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Summary:We introduce the generalized Besov-type space over the Haar basis. We give the two-sided estimate for the norm of functions of the space in terms of their Fourier–Haar coefficients. Also, we establish a criterion for the embedding and some two-sided estimate for the approximation of in the metric of  , with and .
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446622060131