| Title:
|
On the rate of strong summability of double Fourier series (English) |
| Author:
|
Łenski, Włodzimierz |
| Author:
|
Topolewska, Maria |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
123 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
337-363 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
double Fourier series |
| Keyword:
|
strong approximation |
| Keyword:
|
strong means of Marcinkiewicz type |
| Keyword:
|
Cesàro means |
| MSC:
|
40F05 |
| MSC:
|
40G05 |
| MSC:
|
41A17 |
| MSC:
|
42A10 |
| MSC:
|
42B08 |
| idZBL:
|
Zbl 0936.42007 |
| idMR:
|
MR1667108 |
| DOI:
|
10.21136/MB.1998.125967 |
| . |
| Date available:
|
2009-09-24T21:33:00Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125967 |
| . |
| Reference:
|
[1] E. F. Beckenbach R. Bellman: Inequalities.Springer-Verlag, Berlin-Heidelberg-New York, 1965. MR 0192009 |
| Reference:
|
[2] Ju. A. Brudnyj I. J. Gopijengauz: On a theorem of Hardy and Littlewood.Mat. Sb. 52 (1960), 891-894. MR 0120376 |
| Reference:
|
[3] W. Łenski: On the norm-strong approximation of $2 \pi$-periodic functions.Demonstratio Math. 11 (1978), 285-299. MR 0507287 |
| Reference:
|
[4] W. Łenski: On the strong approximation of functions belonging to the space $L^q$ $(1 \leg q \leg \infty)$.Funct. Approx. Comment. Math. 6 (1978), 153-166. Zbl 0385.42002, MR 0548366 |
| Reference:
|
[5] W. Łenski: Strong approximation of double Fourier series.Funct. Approx. Comment. Math. 4 (1976), 71-83. MR 0442594 |
| Reference:
|
[6] D. S. Mitrinowič: Analytic Inequalities.Springer-Verlag, Berlin-Heidelberg-New York, 1970. MR 0274686 |
| Reference:
|
[7] A. Zygmund: Trigonometric series I.Cambridge, 1959. |
| Reference:
|
[8] A. Zygmund: Trigonometric series II.Cambridge, 1959. |
| Reference:
|
[9] L. V. Zhizhiashvili: Conjugate Functions and Trigonometric series.Tbilisi, 1969. MR 0261275 |
| . |
