R-boundedness of smooth operator-valued functions

In 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...

On Besov regularity of Brownian motions in infinite dimensions