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The averaging integral operator between weighted Lebesgue spaces and reverse Hölder inequalities
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SYSNO ASEP 0342832 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title The averaging integral operator between weighted Lebesgue spaces and reverse Hölder inequalities Author(s) Opic, Bohumír (MU-W) SAI Source Title Complex Variables and Elliptic Equations. An International Journal. - : Taylor & Francis - ISSN 1747-6933
Roč. 55, 8-10 (2010), s. 965-972Number of pages 8 s. Language eng - English Country GB - United Kingdom Keywords averaging integral operator ; weighted Lebesque spaces ; weights ; Hardy-type inequalities ; reverse Höldet inequalities Subject RIV BA - General Mathematics R&D Projects GA201/08/0383 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000282807200018 EID SCOPUS 77954651673 DOI 10.1080/17476930903276027 Annotation Let 1 < p ≤ q < +∞ and v, w be weights on (0, +∞) such that v(x)xρ is equivalent to a non-decreasing function on (0, +∞) for some ρ ≥ 0, and ... First, we prove that the operator ... if and only if the operator ... Second, we show that the boundedness of the averaging operator A on the space Lp((0, +∞); v) implies that, for all r > 0, the weight v1-p' satisfies the reverse Hlder inequality over the interval (0, r) with respect to the measure dt, while the weight v satisfies the reverse Hlder inequality over the interval (r, +∞) with respect to the measure t-p dt. As a corollary, we obtain that the boundedness of the averaging operator A on the space Lp((0, +∞); v) is equivalent to the boundedness of the averaging operator A on the space Lp((0, +∞); v1+δ) for some δ > 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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