108 citations · 236 across the 36 of their papers we have counts for
17 papers · 1 filter
The bounds and are sharp
Emiel Lorist, Jan van Neerven
It was proved in the 1980s by Burkholder and Bourgain that, for any Banach space and , the UMD property for is equivalent to boundedness of the Hilbert tran…
Dimension-free -calculus of angle for UMD-valued Ornstein--Uhlenbeck operators
Jan van Neerven
Let , let be a UMD Banach space, let , and let be the generator of the Ornstein--Uhlenbeck semigroup on $L^p(\mathbb R^d,γ_d;…
Necessary conditions for deterministic and stochastic maximal regularity
Emiel Lorist, Jan van Neerven, Mark Veraar +1
We study the role of Banach space geometry in deterministic and stochastic maximal regularity. We first construct an example showing that the UMD assumption in the characterisation…
Lévy measures on Banach spaces
Jan van Neerven, Markus Riedle
We establish an explicit characterisation of Lévy measures on both -spaces and UMD Banach spaces. In the case of -spaces, Lévy measures are characterised by an integrabil…
Spectral multiplier theorems for abstract harmonic oscillators on UMD lattices
Jan van Neerven, Pierre Portal, Himani Sharma
We consider operators acting on a UMD Banach lattice that have the same algebraic structure as the position and momentum operators associated with the harmonic oscillator $-\fr…
Functional Analysis
Jan van Neerven
In this second edition, I have taken the opportunity to improve the presentation in several places, to test and revise the problem sets, and to add some new material.
On conditional expectations in L^p(mu;L^q(nu;X))
Qi Lu, Jan van Neerven
Let and be probability spaces, let be a sub--algebra of the product -algebra , let be…
On the R-boundedness of stochastic convolution operators
Jan van Neerven, Mark Veraar, Lutz Weis
The -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…
The L^p-Poincaré inequality for analytic Ornstein-Uhlenbeck operators
Jan van Neerven
Consider the linear stochastic evolution equation dU(t) = AU(t) + dW_H(t), t\ge 0, where A generates a C_0-semigroup on a Banach space E and W_H is a cylindrical Brownian motion in…
Compactness in the Lebesgue-Bochner spaces L^p(μ;X)
Jan van Neerven
Let (Ω,μ) be a finite measure space, X a Banach space, and let 1\le p<\infty. The aim of this paper is to give an elementary proof of the Diaz--Mayoral theorem that a subset V of L…
Maximal gamma-regularity
Jan van Neerven, Mark Veraar, Lutz Weis
In this paper we prove maximal regularity estimates in "square function spaces" which are commonly used in harmonic analysis, spectral theory, and stochastic analysis. In particula…
The stochastic Weiss conjecture for bounded analytic semigroups
Jamil Abreu, Bernhard Haak, Jan van Neerven
Suppose -A admits a bounded H-infinity calculus of angle less than pi/2 on a Banach space E with Pisier's property (alpha), let B be a bounded linear operator from a Hilbert space…
Pathwise Holder convergence of the implicit Euler scheme for semi-linear SPDEs with multiplicative noise
S. G. Cox, J. M. A. M. van Neerven
In this article we prove pathwise Holder convergence with optimal rates of the implicit Euler scheme for semi-linear parabolic stochastic differential equations with multiplicative…
Non-tangential maximal functions and conical square functions with respect to the Gaussian measure
Jan Maas, Jan van Neerven, Pierre Portal
We study, in with respect to the gaussian measure, non-tangential maximal functions and conical square functions associated with the Ornstein-Uhlenbeck operator by…
Gradient estimates and domain identification for analytic Ornstein-Uhlenbeck operators
Jan Maas, Jan van Neerven
Let (P(t)) be the Ornstein-Uhlenbeck semigroup associated with the stochastic Cauchy problem dU(t) = AU(t)dt + dW_H(t), where A is the generator of a C_0-semigroup (S(t)) on a Bana…
-Radonifying operators -- a survey
Jan van Neerven
We present a survey of the theory of -radonifying operators and their applications to stochastic integration in Banach spaces.
Uniformly gamma-radonifying families of operators and and the stochastic Weiss conjecture
Bernhard H. Haak, Jan van Neerven
We introduce the notion of uniform gamma-radonification of a family of operators, which unifies the notions of R-boundedness of a family of operators and gamma-radonification of an…