On $L^{p}$ integrability and convergence of trigonometric series

• Autorzy: Dansheng Yu , Ping Zhou , Songping Zhou
• Języki publikacji: EN

Abstrakty

EN

We first give a necessary and sufficient condition for $x^{-γ} ϕ(x) ∈ L^{p}$, 1 < p < ∞, 1/p - 1 < γ < 1/p, where ϕ(x) is the sum of either $∑_{k=1}^{∞} a_{k} cos kx$ or $∑_{k=1}^{∞} b_{k} sin kx$, under the condition that {λₙ} (where λₙ is aₙ or bₙ respectively) belongs to the class of so called Mean Value Bounded Variation Sequences (MVBVS). Then we discuss the relations among the Fourier coefficients λₙ and the sum function ϕ(x) under the condition that {λₙ} ∈ MVBVS, and deduce a sharp estimate for the weighted modulus of continuity of ϕ(x) in $L^{p}$ norm.

Kategorie tematyczne

• 42A20: Convergence and absolute convergence of Fourier and trigonometric series
• 42A32: Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 182
• Numer: 3
• Strony: 215-226

Daty

wydano

2007

Twórcy

autor

Dansheng Yu

• Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China
• Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, Antigonish, Nova Scotia Canada, B2G 2W5

autor

Ping Zhou

• Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, Antigonish, Nova Scotia Canada, B2G 2W5

autor

Songping Zhou

• Institute of Mathematics, Zhejiang Sci-Tech University, Xiasha Economic Development Area, Hangzhou, Zhejiang 310018, China
• Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, Antigonish, Nova Scotia Canada, B2G 2W5

Identyfikatory

DOI

10.4064/sm182-3-3