# On the degree of convergence of Borel and Euler means for double Fourier series of functions of bounded variation in Hardy sense

Mathematica Bohemica (1995)

- Volume: 120, Issue: 1, page 1-12
- ISSN: 0862-7959

## Access Full Article

top## Abstract

top## How to cite

topTopolewska, Maria. "On the degree of convergence of Borel and Euler means for double Fourier series of functions of bounded variation in Hardy sense." Mathematica Bohemica 120.1 (1995): 1-12. <http://eudml.org/doc/247809>.

@article{Topolewska1995,

abstract = {For real functions of bounded variation in the Hardy sense, $2\pi $-periodic in each variable, the rates of pointwise convergence of the Borel and Euler means of their Fourier series are estimated.},

author = {Topolewska, Maria},

journal = {Mathematica Bohemica},

keywords = {rate of convergence; bounded variation; rectangular partial sums; double Fourier series; double trigonometric series; Borel means; Euler means; rate of convergence; bounded variation; rectangular partial sums; double Fourier series},

language = {eng},

number = {1},

pages = {1-12},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On the degree of convergence of Borel and Euler means for double Fourier series of functions of bounded variation in Hardy sense},

url = {http://eudml.org/doc/247809},

volume = {120},

year = {1995},

}

TY - JOUR

AU - Topolewska, Maria

TI - On the degree of convergence of Borel and Euler means for double Fourier series of functions of bounded variation in Hardy sense

JO - Mathematica Bohemica

PY - 1995

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 120

IS - 1

SP - 1

EP - 12

AB - For real functions of bounded variation in the Hardy sense, $2\pi $-periodic in each variable, the rates of pointwise convergence of the Borel and Euler means of their Fourier series are estimated.

LA - eng

KW - rate of convergence; bounded variation; rectangular partial sums; double Fourier series; double trigonometric series; Borel means; Euler means; rate of convergence; bounded variation; rectangular partial sums; double Fourier series

UR - http://eudml.org/doc/247809

ER -

## References

top- R. Bojanić, An estimate of the rate of convergence for Fourier series of functions of bounded variation, Publications de L'Institut Mathématique, Nouvelle série 26(40) (1979), 57-60. (1979) MR0572330
- C. K. Chui A. S. B. Holland, 10.1016/0021-9045(83)90066-7, Journal of Approximation Theory 39 (1983), 24-38. (1983) MR0713359DOI10.1016/0021-9045(83)90066-7
- G. H. Hardy, Divergent series, Oxford, 1949. (1949) Zbl0032.05801MR0030620
- J. Marcinkiewicz, On a class of functions and their Fourier series, Collected papers. PWN, Warszawa, 1964, pp. 36-41. (1964)
- R. Taberski, On double integrals and Fourier series, Annales Polon. Math. 15 (1964), 97-115. (1964) Zbl0171.30002MR0167787
- L. Tonelli, Série Trigonometrische, Bologna, 1928. (1928)
- M. Topolewska, On the degree of convergence of Borel and Euler means of trigonometric series, Časopis pro pěstování matematiky 112(3) (1987), 225-232. (1987) Zbl0625.42004MR0905967

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.