The best $$$m$$$-term trigonometric approximations of the classes of periodic multivariate functions of mixed smoothness

K.V. Pozharska; A.S. Romanyuk

doi:10.15421/242520

The best $$$m$$$-term trigonometric approximations of the classes of periodic multivariate functions of mixed smoothness

K.V. Pozharska (Institute of Mathematics of NAS of Ukraine, Chemnitz University of Technology), https://orcid.org/0000-0001-7599-8117
A.S. Romanyuk (Institute of Mathematics of NAS of Ukraine), https://orcid.org/0000-0002-6268-0799

Abstract

Exact in order estimates are obtained for the best $$$m$$$-term trigonometric approximations of the classes of periodic multivariate functions of mixed smoothness (Nikol'skii-Besov $$$B^{\boldsymbol{r}}_{p, \theta}$$$ and Sobolev $$$W^{\boldsymbol{r}}_{p,\boldsymbol{\alpha}}$$$ classes) in the space $$$B_{q,1}$$$, $$$2\leq p<q<\infty$$$. The norm in this space is not weaker than the $$$L_q$$$-norm. The obtained estimates in the multivariate case, in contrast to the univariate, differ in order from the respective estimates in the $$$L_q$$$-space.

Keywords

Nikol'skii-Besov classes; Sobolev classes; periodic functions of mixed smoothness; best $$$m$$$-term trigonometric approximations

MSC 2020

Pri 41A25, Sec 41A46, 41A63

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