R-boundedness of smooth operator-valued functions

الأصل · EN

In this paper we study R-boundedness of operator families T⊂ (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:ᵈ→ (X,Y) which is in a certain Besov space Bᵈ/ʳᵣ,₁(ᵈ;(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.