Jacobi weights, fractional integration, and sharp Ulyanov inequalities

Published 5 Jan 2016 in math.FA | (1601.00814v1)

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.

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