About: Interpolation properties of Besov spaces defined on metric spaces

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Description	Let X = (X, d, μ) be a doubling metric measure space. We define so called Besov spaces B_{p,q}^α(X). We will show that if a doubling metric measure space (X, d, μ) supports a (1, p)-Poincaré inequality, then the Besov space B_{p,q}^α(X) coincides with the real interpolation space (L_{p}(X), KS_{1,p}(X))_{ α ,q}, where KS_{1,p}(X) is the Sobolev space defined by Korevaar and Schoen . This result is used to prove the imbedding theorems. Let X = (X, d, μ) be a doubling metric measure space. We define so called Besov spaces B_{p,q}^α(X). We will show that if a doubling metric measure space (X, d, μ) supports a (1, p)-Poincaré inequality, then the Besov space B_{p,q}^α(X) coincides with the real interpolation space (L_{p}(X), KS_{1,p}(X))_{ α ,q}, where KS_{1,p}(X) is the Sobolev space defined by Korevaar and Schoen . This result is used to prove the imbedding theorems. (en)
Title	Interpolation properties of Besov spaces defined on metric spaces Interpolation properties of Besov spaces defined on metric spaces (en)
skos:prefLabel	Interpolation properties of Besov spaces defined on metric spaces Interpolation properties of Besov spaces defined on metric spaces (en)
skos:notation	RIV/67985840:_____/10:00339255!RIV10-AV0-67985840
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	2
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Gogatishvili, Amiran
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	264604
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/10:00339255
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Besov spaces; Sobolev spaces; real interpolation method; K-functional; metric measure space; doubling measure space; embedding theorems (en)
http://linked.open.../riv/klicoveSlovo	K-functional doubling measure space metric measure space real interpolation method Besov spaces embedding theorems Sobolev spaces
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[3C292D8CA743]
http://linked.open...i/riv/nazevZdroje	Mathematische Nachrichten
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (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	283
http://linked.open...iv/tvurceVysledku	Gogatishvili, Amiran Koskela, P. Shanmugalingam, N.
http://linked.open...ain/vavai/riv/wos	000275649300005
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi
issn	0025-584X
number of pages	17 (xsd:int)

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