Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 in the case that
$\mathcal{T}$ is the range of an operator-valued function $T:\R^d\to
\calL(X,Y)$ 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.

36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ