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

Krasniqi, Xhevat Z., Kórus, Péter, and Móricz, Ferenc. "Necessary conditions for the $L^{p}$-convergence $(0<p<1)$ of single and double trigonometric series." Mathematica Bohemica 139.1 (2014): 75-88. <http://eudml.org/doc/261093>.

@article{Krasniqi2014,
abstract = {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 $H^\{p\}$ and the Bernstein-Zygmund inequalities for the derivatives of trigonometric polynomials and their conjugates in the $L^\{p\}$-metric, where $0<p<1$.},
author = {Krasniqi, Xhevat Z., Kórus, Péter, Móricz, Ferenc},
journal = {Mathematica Bohemica},
keywords = {trigonometric series; Hardy-Littlewood inequality for functions in $H^\{p\}$; Bernstein-Zygmund inequalities for the derivative of trigonometric polynomials in $L^\{p\}$-metric for $0<p<1$; necessary conditions for the convergence in $L^\{p\}$-metric; trigonometric series; Hardy-Littlewood inequality for functions in $H^\{p\}$; ; necessary conditions for the convergence in $L^\{p\}$-metric},
language = {eng},
number = {1},
pages = {75-88},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Necessary conditions for the $L^\{p\}$-convergence $(0<p<1)$ of single and double trigonometric series},
url = {http://eudml.org/doc/261093},
volume = {139},
year = {2014},
}

TY - JOUR
AU - Krasniqi, Xhevat Z.
AU - Kórus, Péter
AU - Móricz, Ferenc
TI - Necessary conditions for the $L^{p}$-convergence $(0<p<1)$ of single and double trigonometric series
JO - Mathematica Bohemica
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 139
IS - 1
SP - 75
EP - 88
AB - 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 $H^{p}$ and the Bernstein-Zygmund inequalities for the derivatives of trigonometric polynomials and their conjugates in the $L^{p}$-metric, where $0<p<1$.
LA - eng
KW - trigonometric series; Hardy-Littlewood inequality for functions in $H^{p}$; Bernstein-Zygmund inequalities for the derivative of trigonometric polynomials in $L^{p}$-metric for $0<p<1$; necessary conditions for the convergence in $L^{p}$-metric; trigonometric series; Hardy-Littlewood inequality for functions in $H^{p}$; ; necessary conditions for the convergence in $L^{p}$-metric
UR - http://eudml.org/doc/261093
ER -