Over the past fifteen years, motivated by regularity problems in evolution equations, there
has been tremendous progress in the analysis of Banach space-valued functions and …

In these lecture notes we report on recent breakthroughs in the functional analytic approach
to maximal regularity for parabolic evolution equations, which set off a wave of activity in the …

HUMMET K. MUSAEV1, 2 Abstract. This paper explores the maximal regularity and
separability properties of abstract differential operator equations in weighted spaces. Using …

This paper presents a brief survey of the theory of stochastic integration in Banach spaces.
Expositions of the stochastic integrals in martingale type 2 spaces and UMD spaces are …

Using notions from the geometry of Banach spaces we introduce square functions $\gamma
(\Omega, X) $ for functions with values in an arbitrary Banach space $ X $. We show that …

We prove a general sparse domination theorem in a space of homogeneous type, in which a
vector-valued operator is controlled pointwise by a positive, local expression called a sparse …

We investigate pointwise multipliers on vector-valued function spaces over R^ d R d,
equipped with Muckenhoupt weights. The main result is that in the natural parameter range …

Evolutionary equations in a Banach space X of the form u. k C 1/. Au/. k/D f. k/; k 2 ZC;./arise
in several branches of science and technology [1, 26, 61, 75, 81, 89, 116, 125, 129, 144 …

We use Fourier multiplier theorems to establish maximal regularity results for a class of
integro-differential equations with infinite delay in Banach spaces. Concrete equations of …

We establish that solitary stationary waves in three dimensional viscous incompressible
fluids are a general phenomenon and that every such solution is a vanishing wave-speed …