Geodesic
Functions with general monotone Fourier coefficients
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 76 (2021) no. 6, pp. 951-1017

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is a study of trigonometric series with general monotone coefficients in the class $\operatorname{GM}(p)$ with $p\geqslant 1$. Sharp estimates are proved for the Fourier coefficients of integrable and continuous functions. Also obtained are optimal results in terms of coefficients for various types of convergence of Fourier series. For $1$ two-sided estimates are obtained for the $L_p$-moduli of smoothness of sums of series with $\operatorname{GM}(p)$-coefficients, as well as for the (quasi-)norms of such sums in Lebesgue, Lorentz, Besov, and Sobolev spaces in terms of Fourier coefficients. Bibliography: 99 titles.
Keywords: functions with general monotone Fourier coefficients; estimates of Fourier coefficients; moduli of smoothness; Lebesgue, Lorentz
Mots-clés : Besov, Sobolev spaces. 
@article{RM_2021_76_6_a0,
     author = {A. S. Belov and M. I. Dyachenko and S. Yu. Tikhonov},
     title = {Functions with general monotone {Fourier} coefficients},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {951--1017},
     publisher = {mathdoc},
     volume = {76},
     number = {6},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2021_76_6_a0/}
}
TY  - JOUR
AU  - A. S. Belov
AU  - M. I. Dyachenko
AU  - S. Yu. Tikhonov
TI  - Functions with general monotone Fourier coefficients
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2021
SP  - 951
EP  - 1017
VL  - 76
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RM_2021_76_6_a0/
LA  - en
ID  - RM_2021_76_6_a0
ER  - 
%0 Journal Article
%A A. S. Belov
%A M. I. Dyachenko
%A S. Yu. Tikhonov
%T Functions with general monotone Fourier coefficients
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2021
%P 951-1017
%V 76
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RM_2021_76_6_a0/
%G en
%F RM_2021_76_6_a0
A. S. Belov; M. I. Dyachenko; S. Yu. Tikhonov. Functions with general monotone Fourier coefficients. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 76 (2021) no. 6, pp. 951-1017. http://geodesic.mathdoc.fr/item/RM_2021_76_6_a0/