R-boundedness of Smooth Operator-valued Functions
نویسندگان
چکیده
In this paper we study R-boundedness of operator families T ⊂ B(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 : Rd → B(X, Y ) which is in a certain Besov space B d/r r,1 (R d;B(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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