The R
-boundedness of certain families of vector-valued stochastic convolution operators with scalar-valued square integrable kernels is the key ingredient in the recent proof of stochastic maximal L p
-regularity, 2<p<∞
, for certain classes of sectorial operators a
...
The R
-boundedness of certain families of vector-valued stochastic convolution operators with scalar-valued square integrable kernels is the key ingredient in the recent proof of stochastic maximal L p
-regularity, 2<p<∞
, for certain classes of sectorial operators acting on spaces X=L q (μ)
, 2≤q<∞
. This paper presents a systematic study of R
-boundedness of such families. Our main result generalises the afore-mentioned R
-boundedness result to a larger class of Banach lattices X
and relates it to the ℓ 1
-boundedness of an associated class of deterministic convolution operators. We also establish an intimate relationship between the ℓ 1
-boundedness of these operators and the boundedness of the X
-valued maximal function. This analysis leads, quite surprisingly, to an example showing that R
-boundedness of stochastic convolution operators fails in certain UMD Banach lattices with type 2
.@en
