About: Weighted estimates for the averaging integral operator

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Let 1 < p <= q < +infinity and let v, w be weights on (0, +infinity) satisfying%22 (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)). Let 1 < p <= q < +infinity and let v, w be weights on (0, +infinity) satisfying%22 (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)). (en)
Title	Weighted estimates for the averaging integral operator Weighted estimates for the averaging integral operator (en)
skos:prefLabel	Weighted estimates for the averaging integral operator Weighted estimates for the averaging integral operator (en)
skos:notation	RIV/67985840:_____/10:00342853!RIV11-GA0-67985840
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/05/2033), P(GA201/08/0383), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Rákosník, Jiří 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	298714
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/10:00342853
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	averaging integral operator; weighted Lebesgue spaces; weights (en)
http://linked.open.../riv/klicoveSlovo	weighted Lebesgue spaces averaging integral operator weights
http://linked.open...odStatuVydavatele	ES - Španělské království
http://linked.open...ontrolniKodProRIV	[99471813B526]
http://linked.open...i/riv/nazevZdroje	Collectanea Mathematica
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Function Spaces, Weighted Inequalities and Interpolation Function Spaces, Weighted Inequalities and Real Interpolation
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	61
http://linked.open...iv/tvurceVysledku	Rákosník, Jiří Opic, Bohumír
http://linked.open...ain/vavai/riv/wos	000282670300002
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi
issn	0010-0757
number of pages	10 (xsd:int)

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