Geodesic
Integrability and continuity of functions represented by trigonometric series: coefficients criteria
Mikhail Dyachenko1 ; Sergey Tikhonov2
1Moscow State University Vorob'evy Gory Moscow 119992, Russia
2ICREA and Centre de Recerca Matemática Apartat 50 08193 Bellaterra, Barcelona, Spain
Studia Mathematica, Tome 193 (2009) no. 3, pp. 285-306
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

We study weighted $L_p$-integrability ($1\le p\infty $) of trigonometric series. It is shown how the integrability of a function with weight $x^{-\alpha }$ depends on some regularity conditions on Fourier coefficients. Criteria for the uniform convergence of trigonometric series in terms of their coefficients are also studied.
DOI : 10.4064/sm193-3-5
Keywords: study weighted p integrability infty trigonometric series shown integrability function weight alpha depends regularity conditions fourier coefficients criteria uniform convergence trigonometric series terms their coefficients studied

Mikhail Dyachenko  1   ; Sergey Tikhonov  2

1 Moscow State University Vorob'evy Gory Moscow 119992, Russia
2 ICREA and Centre de Recerca Matemática Apartat 50 08193 Bellaterra, Barcelona, Spain 
@article{10_4064_sm193_3_5,
     author = {Mikhail Dyachenko and Sergey Tikhonov},
     title = {Integrability and continuity of functions represented by
 trigonometric series: coefficients criteria},
     journal = {Studia Mathematica},
     pages = {285--306},
     year = {2009},
     volume = {193},
     number = {3},
     doi = {10.4064/sm193-3-5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm193-3-5/}
}
TY  - JOUR
AU  - Mikhail Dyachenko
AU  - Sergey Tikhonov
TI  - Integrability and continuity of functions represented by
 trigonometric series: coefficients criteria
JO  - Studia Mathematica
PY  - 2009
SP  - 285
EP  - 306
VL  - 193
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm193-3-5/
DO  - 10.4064/sm193-3-5
LA  - en
ID  - 10_4064_sm193_3_5
ER  - 
%0 Journal Article
%A Mikhail Dyachenko
%A Sergey Tikhonov
%T Integrability and continuity of functions represented by
 trigonometric series: coefficients criteria
%J Studia Mathematica
%D 2009
%P 285-306
%V 193
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/sm193-3-5/
%R 10.4064/sm193-3-5
%G en
%F 10_4064_sm193_3_5
Mikhail Dyachenko; Sergey Tikhonov. Integrability and continuity of functions represented by
 trigonometric series: coefficients criteria. Studia Mathematica, Tome 193 (2009) no. 3, pp. 285-306. doi: 10.4064/sm193-3-5

Cité par Sources :