Weighted integrability of double cosine series with nonnegative coefficients

• Autorzy: Chang-Pao Chen , Ming-Chuan Chen
• Języki publikacji: EN

Abstrakty

EN

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].

Kategorie tematyczne

• 42B05: Fourier series and coefficients
• 42A32: Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 156
• Numer: 2
• Strony: 133-141

Daty

wydano

2003

Twórcy

autor

Chang-Pao Chen

• Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 300, Republic of China

autor

Ming-Chuan Chen

• Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 300, Republic of China

Identyfikatory

DOI

10.4064/sm156-2-4