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The averaging integral operator between weighted Lebesgue spaces and reverse Hölder inequalities
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SYSNO ASEP 0342832 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název The averaging integral operator between weighted Lebesgue spaces and reverse Hölder inequalities Tvůrce(i) Opic, Bohumír (MU-W) SAI Zdroj.dok. Complex Variables and Elliptic Equations. An International Journal. - : Taylor & Francis - ISSN 1747-6933
Roč. 55, 8-10 (2010), s. 965-972Poč.str. 8 s. Jazyk dok. eng - angličtina Země vyd. GB - Velká Británie Klíč. slova averaging integral operator ; weighted Lebesque spaces ; weights ; Hardy-type inequalities ; reverse Höldet inequalities Vědní obor RIV BA - Obecná matematika CEP GA201/08/0383 GA ČR - Grantová agentura ČR CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000282807200018 EID SCOPUS 77954651673 DOI 10.1080/17476930903276027 Anotace 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. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2011
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