Jacobi weights, fractional integration, and sharp Ulyanov inequalities
arXiv:1601.00814 · doi:10.1016/j.jat.2014.05.005
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.