On the Nörlund means of Vilenkin-Fourier series

István Blahota; Lars-Erik Persson; Giorgi Tephnadze

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 4, page 983-1002
  • ISSN: 0011-4642

Abstract

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We prove and discuss some new ( H p , L p ) -type inequalities of weighted maximal operators of Vilenkin-Nörlund means with non-increasing coefficients { q k : k ≥ 0 } . These results are the best possible in a special sense. As applications, some well-known as well as new results are pointed out in the theory of strong convergence of such Vilenkin-Nörlund means. To fulfil our main aims we also prove some new estimates of independent interest for the kernels of these summability results. In the special cases of general Nörlund means t n with non-increasing coefficients analogous results can be obtained for Fejér and Cesàro means by choosing the generating sequence { q k : k ≥ 0 } in an appropriate way.

How to cite

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Blahota, István, Persson, Lars-Erik, and Tephnadze, Giorgi. "On the Nörlund means of Vilenkin-Fourier series." Czechoslovak Mathematical Journal 65.4 (2015): 983-1002. <http://eudml.org/doc/276158>.

@article{Blahota2015,
abstract = {We prove and discuss some new $( H_\{p\},L_\{p\})$-type inequalities of weighted maximal operators of Vilenkin-Nörlund means with non-increasing coefficients $\lbrace q_\{k\}\colon k\ge 0\rbrace $. These results are the best possible in a special sense. As applications, some well-known as well as new results are pointed out in the theory of strong convergence of such Vilenkin-Nörlund means. To fulfil our main aims we also prove some new estimates of independent interest for the kernels of these summability results. In the special cases of general Nörlund means $t_\{n\}$ with non-increasing coefficients analogous results can be obtained for Fejér and Cesàro means by choosing the generating sequence $\lbrace q_\{k\}\colon k\ge 0\rbrace $ in an appropriate way.},
author = {Blahota, István, Persson, Lars-Erik, Tephnadze, Giorgi},
journal = {Czechoslovak Mathematical Journal},
keywords = {Vilenkin system; Vilenkin group; Nörlund means; martingale Hardy space; maximal operator; Vilenkin-Fourier series; strong convergence; inequality},
language = {eng},
number = {4},
pages = {983-1002},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the Nörlund means of Vilenkin-Fourier series},
url = {http://eudml.org/doc/276158},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Blahota, István
AU - Persson, Lars-Erik
AU - Tephnadze, Giorgi
TI - On the Nörlund means of Vilenkin-Fourier series
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 4
SP - 983
EP - 1002
AB - We prove and discuss some new $( H_{p},L_{p})$-type inequalities of weighted maximal operators of Vilenkin-Nörlund means with non-increasing coefficients $\lbrace q_{k}\colon k\ge 0\rbrace $. These results are the best possible in a special sense. As applications, some well-known as well as new results are pointed out in the theory of strong convergence of such Vilenkin-Nörlund means. To fulfil our main aims we also prove some new estimates of independent interest for the kernels of these summability results. In the special cases of general Nörlund means $t_{n}$ with non-increasing coefficients analogous results can be obtained for Fejér and Cesàro means by choosing the generating sequence $\lbrace q_{k}\colon k\ge 0\rbrace $ in an appropriate way.
LA - eng
KW - Vilenkin system; Vilenkin group; Nörlund means; martingale Hardy space; maximal operator; Vilenkin-Fourier series; strong convergence; inequality
UR - http://eudml.org/doc/276158
ER -

References

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