Jacobi weights, fractional integration, and sharp Ulyanov inequalities
Functional Analysis
2016-01-06 v1
Abstract
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.
Cite
@article{arxiv.1601.00814,
title = {Jacobi weights, fractional integration, and sharp Ulyanov inequalities},
author = {Polina Glazyrina and Sergey Tikhonov},
journal= {arXiv preprint arXiv:1601.00814},
year = {2016}
}