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)

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