We prove a Mihlin–type multiplier theorem for operator–valued multiplier functions on UMD–
spaces. The essential assumption is R–boundedness of the multiplier function. As an …

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 …

Evolution equations and their applications in physical and life sciences Page 1 A New
Approach to Maximal Lp-Regularity LUTZ WEIS Universitat Karlsruhe, Mathematisches Institut …

Let $ X $ be a metric space with doubling measure, and $ L $ be a non-negative, self-adjoint
operator satisfying Davies-Gaffney bounds on $ L^ 2 (X) $. In this article we present a theory …

We develop a very general operator-valued functional calculus for operators with an H^∞-
calculus. We then apply this to the joint functional calculus of two sectorial operators when …

Let $ L $ be the infinitesimal generator of an analytic semigroup on $ L^ 2 ({\mathbb R}^ n) $
with suitable upper bounds on its heat kernels. Auscher, Duong, and McIntosh defined a …

This is a survey on recent developments of the theory of one-parameter semigroups and
evolution equations with special emphasis on functional calculus and kernel estimates. Also …

Gaussian heat kernel upper bounds via the Phragmén–Lindelöf theorem Page 1 Proc.
London Math. Soc. (3) 96 (2008) 507–544 Cо2007 London Mathematical Society doi:10.1112/plms/pdm050 …

Let X be a space of homogeneous type and L be a nonnegative self-adjoint operator on L2
(X) satisfying Gaussian upper bounds on its heat kernels. In this paper, we develop the …

The main goal of the paper is to establish time semidiscrete and space-time fully discrete
maximal parabolic regularity for the time discontinuous Galerkin solution of linear parabolic …