R-boundedness of smooth operator-valued functions

2008/04/21 by Mark Veraar, Tuomas Hytönen, Veraar, Mark +2
Economics, Econometrics and Finance · Mathematics · #46B09 #46E35 #46E40 #47B99 #60B05 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #Stochastic processes and financial applications #math.FA #math.PR #msc:46B09 #msc:46E35 #msc:46E40 #msc:47B99 #msc:60B05

paper · pdf · doi:10.48550/arxiv.0804.3313

some typos corrected

openalex publication_date 2008/04/21 · arxiv created 2009/01/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study R-boundedness of operator families T⊂ \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 T is the range of an operator-valued function T:\R^d→ \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.

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