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arXiv · 1601.00814

Jacobi weights, fractional integration, and sharp Ulyanov inequalities

Polina Glazyrina·Sergey Tikhonov
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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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BibTeXRIS

Polina Glazyrina, Sergey Tikhonov. 2016-01-05. Jacobi weights, fractional integration, and sharp Ulyanov inequalities. https://doi.org/10.1016/j.jat.2014.05.005

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