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 :. 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. (2000). Primary 47B99; Secondary 46B09, 46E35, 46E40, 60B05.
Mathematics Subject Classification