On the rate of strong summability of double Fourier series

Włodzimierz Łenski; Maria Topolewska

Mathematica Bohemica (1998)

  • Volume: 123, Issue: 4, page 337-363
  • ISSN: 0862-7959

Abstract

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Estimates of the strong means of Marcinkiewicz type with the Cesaro means of negative order in one of the variables instead of square partial sums are obtained by characteristics constructed on the basis of moduli of continuity.

How to cite

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Łenski, Włodzimierz, and Topolewska, Maria. "On the rate of strong summability of double Fourier series." Mathematica Bohemica 123.4 (1998): 337-363. <http://eudml.org/doc/248306>.

@article{Łenski1998,
abstract = {Estimates of the strong means of Marcinkiewicz type with the Cesaro means of negative order in one of the variables instead of square partial sums are obtained by characteristics constructed on the basis of moduli of continuity.},
author = {Łenski, Włodzimierz, Topolewska, Maria},
journal = {Mathematica Bohemica},
keywords = {double Fourier series; strong approximation; strong means of Marcinkiewicz type; Cesàro means; double Fourier series; strong approximation; strong means of Marcinkiewicz type; Cesàro means},
language = {eng},
number = {4},
pages = {337-363},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the rate of strong summability of double Fourier series},
url = {http://eudml.org/doc/248306},
volume = {123},
year = {1998},
}

TY - JOUR
AU - Łenski, Włodzimierz
AU - Topolewska, Maria
TI - On the rate of strong summability of double Fourier series
JO - Mathematica Bohemica
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 123
IS - 4
SP - 337
EP - 363
AB - Estimates of the strong means of Marcinkiewicz type with the Cesaro means of negative order in one of the variables instead of square partial sums are obtained by characteristics constructed on the basis of moduli of continuity.
LA - eng
KW - double Fourier series; strong approximation; strong means of Marcinkiewicz type; Cesàro means; double Fourier series; strong approximation; strong means of Marcinkiewicz type; Cesàro means
UR - http://eudml.org/doc/248306
ER -

References

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  1. E. F. Beckenbach R. Bellman, Inequalities, Springer-Verlag, Berlin-Heidelberg-New York, 1965. (1965) MR0192009
  2. Ju. A. Brudnyj I. J. Gopijengauz, On a theorem of Hardy and Littlewood, Mat. Sb. 52 (1960), 891-894. (1960) MR0120376
  3. W. Łenski, On the norm-strong approximation of 2 π -periodic functions, Demonstratio Math. 11 (1978), 285-299. (1978) MR0507287
  4. W. Łenski, On the strong approximation of functions belonging to the space L q ( 1 q ∞ ) , Funct. Approx. Comment. Math. 6 (1978), 153-166. (1978) Zbl0385.42002MR0548366
  5. W. Łenski, Strong approximation of double Fourier series, Funct. Approx. Comment. Math. 4 (1976), 71-83. (1976) MR0442594
  6. D. S. Mitrinowič, Analytic Inequalities, Springer-Verlag, Berlin-Heidelberg-New York, 1970. (1970) MR0274686
  7. A. Zygmund, Trigonometric series I, Cambridge, 1959. (1959) 
  8. A. Zygmund, Trigonometric series II, Cambridge, 1959. (1959) 
  9. L. V. Zhizhiashvili, Conjugate Functions and Trigonometric series, Tbilisi, 1969. (1969) MR0261275

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