Pointwise multipliers for Sobolev and Besov spaces of dominating mixed smoothness

Pointwise Multipliers of Besov Spaces of Smoothness Zero and Spaces of Continuous Functions

Function spaces with dominating mixed smoothness

Acknowledgements I would like to express my deepest appreciation to my supervisors Professor Hans-Jürgen Schmeisser and Professor Winfried Sickel for their support and many hints and comments. I thank also Professor Hans Triebel for many valuable discussions on the topic of this work.

Optimal cubature in Besov spaces with dominating mixed smoothness on the unit square

We prove new optimal bounds for the error of numerical integration in bivariate Besov spaces with dominating mixed order r. The results essentially improve on the so far best known upper bound achieved by using cubature formulas taking points from a sparse grid. Motivated by Hinrichs’ observation that Hammersley type point sets provide optimal discrepancy estimates in Besov spaces with mixed sm...

Commutators for Fourier multipliers on Besov Spaces

The mapping properties of commutators [T,M ] = TM −MT , for operators between function spaces, and their various generalizations play an important role in harmonic analysis, PDE, interpolation theory and other related areas. A typical situation arises when M = Mb is the pointwise multiplication by a function b and T is a Calderón–Zygmund operator on R. Then well– known results of A.P. Calderón ...

General Hörmander and Mikhlin Conditions for Multipliers of Besov Spaces

Abstract. Here a new condition for the geometry of Banach spaces is introduced and the operator–valued Fourier multiplier theorems in weighted Besov spaces are obtained. Particularly, connections between the geometry of Banach spaces and Hörmander-Mikhlin conditions are established. As an application of main results the regularity properties of degenerate elliptic differential operator equation...