Jacobi weights, fractional integration, and sharp Ulyanov inequalities

JOURNAL OF APPROXIMATION THEORY

卷:195

Article

Glazyrina, Polina¹  Tikhonov, Sergey^2,3 

[1] Ural Fed Univ, Subdept Math Anal & Theory Funct, Ekaterinburg 620083, Russia

[2] ICREA, Barcelona 08193, Spain

[3] Ctr Recerca Matemat, Barcelona 08193, Spain

关键词: Jacobi weights;    Landau type inequalities;    Hardy-Littlewood type inequalities;    K-functionals;    Ditzian-Totik moduli of smoothness;    Sharp Ulyanov inequality;   

DOI  :  10.1016/j.jat.2014.05.005

来源: Elsevier

【 摘 要 】

We consider functions L-P-integrable with Jacobi weights on [-1, 1] and prove Hardy-Littlewood type inequalities for fractional integrals. As applications, we obtain the sharp (L-p,L-q) Ulyanov-type inequalities for the Ditzian-Totik moduli of smoothness and the K-functionals of fractional order. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free