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Weighted estimates for the averaging integral operator
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SYSNO ASEP 0342853 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Weighted estimates for the averaging integral operator Author(s) Opic, Bohumír (MU-W) SAI
Rákosník, Jiří (MU-W) RID, SAI, ORCIDSource Title Collectanea Mathematica. - : Springer - ISSN 0010-0757
Roč. 61, č. 3 (2010), s. 253-262Number of pages 10 s. Language eng - English Country ES - Spain Keywords averaging integral operator ; weighted Lebesgue spaces ; weights Subject RIV BA - General Mathematics R&D Projects GA201/05/2033 GA ČR - Czech Science Foundation (CSF) GA201/08/0383 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000282670300002 EID SCOPUS 77953307148 DOI 10.1007/BF03191231 Annotation Let 1 < p <= q < +infinity and let v, w be weights on (0, +infinity) satisfying" (star) v(x)x(rho) is equivalent to a non-decreasing function on (0, +infinity) for some rho >= 0 and w(x)x](1/q) approximate to [v(x)x](1/p) for all x is an element of (0, +infinity), We prove that if the averaging operator (Af)(x) = 1/x integral(x)(0) f(t)dt, x is an element of (0, +infinity), is bounded from the weighted Lebesgue space L-p(0, +infinity), v) into the weighted Lebesgue space L-q((0, +infinity); w), then there exists epsilon(0) is an element of (0, p - 1) such that the space Lq-epsilon q/p((0, +infinity), w(x)(1+delta)x(delta(1-q/p))x(gamma q/p)) for all epsilon, delta, gamma is an element of [0, epsilon(0)). Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2011
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