About: The averaging integral operator between weighted Lebesgue spaces and reverse Hölder inequalities

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	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. 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. (en)
Title	The averaging integral operator between weighted Lebesgue spaces and reverse Hölder inequalities The averaging integral operator between weighted Lebesgue spaces and reverse Hölder inequalities (en)
skos:prefLabel	The averaging integral operator between weighted Lebesgue spaces and reverse Hölder inequalities The averaging integral operator between weighted Lebesgue spaces and reverse Hölder inequalities (en)
skos:notation	RIV/67985840:_____/10:00342832!RIV11-GA0-67985840
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/08/0383), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika	8-10
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Opic, Bohumír
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	248290
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/10:00342832
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	averaging integral operator; weighted Lebesque spaces; weights; Hardy-type inequalities; reverse Höldet inequalities (en)
http://linked.open.../riv/klicoveSlovo	averaging integral operator reverse Höldet inequalities weighted Lebesque spaces Hardy-type inequalities weights
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[91B112BF36EC]
http://linked.open...i/riv/nazevZdroje	Complex Variables and Elliptic Equations. An International Journal
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Function Spaces, Weighted Inequalities and Interpolation
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	55
http://linked.open...iv/tvurceVysledku	Opic, Bohumír
http://linked.open...ain/vavai/riv/wos	000282807200018
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi
issn	1747-6933
number of pages	8 (xsd:int)
is http://linked.open...avai/riv/vysledek of	The averaging integral operator between weighted Lebesgue spaces and reverse Hölder inequalities The averaging integral operator between weighted Lebesgue spaces and reverse Hölder inequalities The averaging integral operator between weighted Lebesgue spaces and reverse Hölder inequalities

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