Necessary conditions for the L p -convergence (0 < p < 1) of single and double trigonometric series

Title:

Necessary conditions for the L p -convergence (0 < p < 1) of single and double trigonometric series

Creator:

Krasniqi, Xhevat Z., Kórus, Péter, and Móricz, Ferenc

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:06601ee0-cd58-4a2c-8b40-62c2597dee37
uuid:06601ee0-cd58-4a2c-8b40-62c2597dee37

Subject:

trigonometric series, Hardy-Littlewood inequality for functions in Hp, Bernstein-Zygmund inequalities for the derivative of trigonometric polynomials in L p - metric for 0 < p < 1, and necessary conditions for the convergence in L p -metric

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We give necessary conditions in terms of the coefficients for the convergence of a double trigonometric series in the L p -metric, where 0 < p < 1. The results and their proofs have been motivated by the recent papers of A. S. Belov (2008) and F. Móricz (2010). Our basic tools in the proofs are the Hardy-Littlewood inequality for functions in Hp and the Bernstein-Zygmund inequalities for the derivatives of trigonometric polynomials and their conjugates in the L p -metric, where 0 < p < 1.

Language:

English

Rights:

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

Coverage:

75-88

Source:

Mathematica bohemica | 2014 Volume:139 | Number:1

Harvested from:

CDK

Metadata only:

false