Jacobi weights, fractional integration, and sharp Ulyanov inequalities

Glazyrina, P.; Tikhonov, S.

doi:10.1016/j.jat.2014.05.005

Please use this identifier to cite or link to this item: http://elar.urfu.ru/handle/10995/75439

Title:	Jacobi weights, fractional integration, and sharp Ulyanov inequalities
Authors:	Glazyrina, P. Tikhonov, S.
Issue Date:	2015
Publisher:	Academic Press Inc.
Citation:	Glazyrina P. Jacobi weights, fractional integration, and sharp Ulyanov inequalities / P. Glazyrina, S. Tikhonov // Journal of Approximation Theory. — 2015. — Vol. 195. — P. 122-140.
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. © 2014 Elsevier Inc.
Keywords:	DITZIAN-TOTIK MODULI OF SMOOTHNESS HARDY-LITTLEWOOD TYPE INEQUALITIES JACOBI WEIGHTS K-FUNCTIONALS LANDAU TYPE INEQUALITIES SHARP ULYANOV INEQUALITY
URI:	http://elar.urfu.ru/handle/10995/75439
Access:	info:eu-repo/semantics/openAccess
SCOPUS ID:	84939883328
WOS ID:	000355038700008
PURE ID:	314138
ISSN:	0021-9045
DOI:	10.1016/j.jat.2014.05.005
metadata.dc.description.sponsorship:	The authors would like to thank F. Dai, Z. Ditzian, and G. Mastroianni for fruitful discussions and useful comments on the fractional K -functionals, and the referee for reading the paper carefully and several valuable comments. The first author was supported by the Ural Federal University development program with the financial support of young scientists and by the Joint Project of IMM UB RAS and IM SB RAS 12-C-1-1018. The second author was partially supported by MTM 2011-27637, 2009 SGR 1303, RFFI 13-01-00043, and NSH-979.2012.1.
Appears in Collections:	Научные публикации ученых УрФУ, проиндексированные в SCOPUS и WoS CC

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