Weighted integrability of double cosine series with nonnegative coefficients

Chang-Pao Chen, and Ming-Chuan Chen. "Weighted integrability of double cosine series with nonnegative coefficients." Studia Mathematica 156.2 (2003): 133-141. <http://eudml.org/doc/284752>.

@article{Chang2003,
abstract = {Let $f_\{c\}(x,y) ≡ ∑_\{j=1\}^\{∞\} ∑_\{k=1\}^\{∞\} a_\{jk\}(1 - cos jx)(1 - cos ky)$ with $a_\{jk\} ≥ 0$ for all j,k ≥ 1. We estimate the integral $∫_\{0\}^\{π\}∫_\{0\}^\{π\} x^\{α-1\} y^\{β-1\} ϕ(f_\{c\}(x,y)) dxdy$ in terms of the coefficients $a_\{jk\}$, where α, β ∈ ℝ and ϕ: [0,∞] → [0,∞]. Our results can be regarded as the trigonometric analogues of those of Mazhar and Móricz [MM]. They generalize and extend Boas [B, Theorem 6.7].},
author = {Chang-Pao Chen, Ming-Chuan Chen},
journal = {Studia Mathematica},
keywords = {double cosine series; weight; integrability; nonnegative coefficients},
language = {eng},
number = {2},
pages = {133-141},
title = {Weighted integrability of double cosine series with nonnegative coefficients},
url = {http://eudml.org/doc/284752},
volume = {156},
year = {2003},
}

TY - JOUR
AU - Chang-Pao Chen
AU - Ming-Chuan Chen
TI - Weighted integrability of double cosine series with nonnegative coefficients
JO - Studia Mathematica
PY - 2003
VL - 156
IS - 2
SP - 133
EP - 141
AB - Let $f_{c}(x,y) ≡ ∑_{j=1}^{∞} ∑_{k=1}^{∞} a_{jk}(1 - cos jx)(1 - cos ky)$ with $a_{jk} ≥ 0$ for all j,k ≥ 1. We estimate the integral $∫_{0}^{π}∫_{0}^{π} x^{α-1} y^{β-1} ϕ(f_{c}(x,y)) dxdy$ in terms of the coefficients $a_{jk}$, where α, β ∈ ℝ and ϕ: [0,∞] → [0,∞]. Our results can be regarded as the trigonometric analogues of those of Mazhar and Móricz [MM]. They generalize and extend Boas [B, Theorem 6.7].
LA - eng
KW - double cosine series; weight; integrability; nonnegative coefficients
UR - http://eudml.org/doc/284752
ER -