On the Nörlund means of Vilenkin-Fourier series

Title:

On the Nörlund means of Vilenkin-Fourier series

Creator:

Blahota, István, Persson, Lars-Erik, and Tephnadze, Giorgi

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:e0912af4-2c51-4d75-8684-f678b8022713
uuid:e0912af4-2c51-4d75-8684-f678b8022713
issn:0011-4642

Subject:

matematika, mathematics, Vilenkin system, Vilenkin group, Nörlund means, martingale Hardy space, maximal operator, Vilenkin-Fourier series, strong convergence, inequality, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

We prove and discuss some new (Hp,Lp)-type inequalities of weighted maximal operators of Vilenkin-Nörlund means with non-increasing coefficients {q_{k}:k\geqslant 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 tn with non-increasing coefficients analogous results can be obtained for Fejér and Cesàro means by choosing the generating sequence {q_{k}:k\geqslant 0} in an appropriate way., István Blahota, Lars-Erik Persson, Giorgi Tephnadze., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

983-1002

Source:

Czechoslovak Mathematical Journal | 2015 Volume:65 | Number:4

Harvested from:

CDK

Metadata only:

false