R-boundedness of smooth operator-valued functions

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dc.creatorVeraar, Mark
dc.creatorHytonen, Tuomas
dc.date2008-04-21
dc.date2009-01-08
dc.date.accessioned2026-07-07T12:26:54Z
dc.date.available2026-07-07T12:26:54Z
dc.descriptionIn this paper we study $R$-boundedness of operator families $\mathcal{T}\subset \calL(X,Y)$, where $X$ and $Y$ are Banach spaces. Under cotype and type assumptions on $X$ and $Y$ we give sufficient conditions for $R$-boundedness. In the first part we show that certain integral operator are $R$-bounded. This will be used to obtain $R$-boundedness in the case that $\mathcal{T}$ is the range of an operator-valued function $T:\R^d\to \calL(X,Y)$ which is in a certain Besov space $B^{d/r}_{r,1}(\R^d;\calL(X,Y))$. The results will be applied to obtain $R$-boundedness of semigroups and evolution families, and to obtain sufficient conditions for existence of solutions for stochastic Cauchy problems.
dc.descriptionsome typos corrected
dc.identifierhttps://arxiv.org/abs/0804.3313
dc.identifierhttp://arxiv.org/abs/0804.3313
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/215034
dc.subjectFunctional Analysis
dc.subjectProbability
dc.subject47B99; 46B09; 46E35; 46E40; 60B05
dc.titleR-boundedness of smooth operator-valued functions
dc.typetext

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