29 citations · 109 across the 14 of their papers we have counts for
16 papers
Weighted Estimates for Operator-Valued Fourier Multipliers
Stephan Fackler, Tuomas P. Hytönen, Nick Lindemulder
We establish Littlewood-Paley decompositions for Muckenhoupt weights in the setting of UMD spaces. As a consequence we obtain two-weight variants of the Mikhlin multiplier theorem…
Off-diagonal sharp two-weight estimates for sparse operators
Stephan Fackler, Tuomas P. Hytönen
For a class of sparse operators including majorants of singular integral, square function, and fractional integral operators in a uniform manner, we prove off-diagonal two-weight e…
A Toolkit for Constructing Dilations on Banach Spaces
Stephan Fackler, Jochen Glück
We present a completely new structure theoretic approach to the dilation theory of linear operators. Our main result is the following theorem: if is a super-reflexive Banach sp…
J. L. Lions' Problem on Maximal Regularity
Wolfgang Arendt, Dominik Dier, Stephan Fackler
This is a survey on recent progress concerning maximal regularity of non-autonomous equations governed by time-dependent forms on a Hilbert space. It also contains two new results…
Non-Autonomous Maximal -Regularity under Fractional Sobolev Regularity in Time
Stephan Fackler
We prove non-autonomous maximal -regularity results on UMD spaces replacing the common Hölder assumption by a weaker fractional Sobolev regularity in time. This generalizes re…
Non-Autonomous Maximal Regularity for Forms Given by Elliptic Operators of Bounded Variation
Stephan Fackler
We show maximal -regularity for non-autonomous Cauchy problems provided the trace spaces are stable in some parameterized sense and the time dependence is of bounded variation…
A Short Counterexample to the Inverse Generator Problem on non-Hilbertian Reflexive -spaces
Stephan Fackler
We show that the bilateral shift group on for provides a counterexample to the inverse generator problem.
J.-L. Lions' Problem Concerning Maximal Regularity of Equations Governed by Non-Autonomous Forms
Stephan Fackler
An old problem due to J.-L. Lions going back to the 1960s asks whether the abstract Cauchy problem associated to non-autonomous forms has maximal regularity if the time dependence…
Non-Autonomous Maximal -Regularity for Rough Divergence Form Elliptic Operators
Stephan Fackler
We obtain maximal regularity estimates for time dependent second order elliptic operators in divergence form with rough dependencies in the spatial variables.
Isometric dilations and calculus for bounded analytic semigroups and Ritt operators
Cédric Arhancet, Stephan Fackler, Christian Le Merdy
We show that any bounded analytic semigroup on (with ) whose negative generator admits a bounded functional calculus with respect to some angle $< π/…
Maximal Regularity: Positive Counterexamples on UMD-Banach Lattices and Exact Intervals for the Negative Solution of the Extrapolation Problem
Stephan Fackler
Using methods from Banach space theory, we prove two new structural results on maximal regularity. The first says that there exist positive analytic semigroups on UMD-Banach lattic…
Regularity Properties of Sectorial Operators: Counterexamples and Open Problems
Stephan Fackler
We give a survey on the different regularity properties of sectorial operators on Banach spaces. We present the main results and open questions in the theory and then concentrate o…
Local Strong Solutions for the Non-Linear Thermoelastic Plate Equation on Rectangular Domains in -Spaces
Stephan Fackler, Tobias Nau
We consider the non-linear thermoelastic plate equation in rectangular domains . More precisely, is considered to be given as the Cartesian product of whole or half spaces a…
On the structure of semigroups on with a bounded -calculus
Stephan Fackler
We show that a bounded analytic semigroup on an -space has a bounded -calculus for some if and only if the semigroup can be obtained, after res…
The Kalton-Lancien Theorem Revisited: Maximal Regularity does not extrapolate
Stephan Fackler
We give a new more explicit proof of a result by Kalton & Lancien stating that on each Banach space with an unconditional basis not isomorphic to a Hilbert space there exists a gen…
Regularity of Semigroups via the Asymptotic Behaviour at Zero
Stephan Fackler
An interesting result by T. Kato and A. Pazy says that a contractive semigroup (T(t)) on a uniformly convex space X is holomorphic iff limsup_{t \downarrow 0} ||T(t)-Id|| < 2. We s…