Jacobi weights, fractional integration, and sharp Ulyanov inequalities
Abstract
We consider functions Lp-integrable with Jacobi weights on [-1,1] and prove Hardy--Littlewood type inequalities for fractional integrals. As applications, we obtain the sharp (Lp, Lq) Ulyanov-type inequalities for the Ditzian--Totik moduli of smoothness and the K-functionals of fractional order.
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