Function Spaces with Dominating Mixed Smoothness

  title={Function Spaces with Dominating Mixed Smoothness},
  author={Hans Triebel},
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. 
Pointwise multipliers for Besov spaces of dominating mixed smoothness - II
We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes Sp,qrB(ℝd) with respect to pointwise
Rate-optimal sparse approximation of compact break-of-scale embeddings
Hyperbolic wavelets are used to introduce corresponding new spaces of Besov- and Triebel-Lizorkin-type to particularly cover the energy norm approximation of functions with dominating mixed smoothness.
Adaptive sampling recovery of functions with higher mixed regularity
The Faber spline system from [14] is tensorized to prove sequence space isomorphisms for multivariate function spaces with higher mixed regularity and the solution of Problem 3.13 in the Triebel monograph is presented.
Sample paths of white noise in spaces with dominating mixed smoothness
The sample paths of white noise are proved to be elements of certain Besov spaces with dominating mixed smoothness. Unlike in isotropic spaces, here the regularity does not get worse with increasing
Turing patterns, Lengyel–Epstein systems and Faber splines
  • H. Triebel
  • Computer Science
    Banach Center Publications
  • 2019
This paper deals with the Lengyel–Epstein CIMA (chlorite-iodide-malonic acid) system of non-linear parabolic equations in the context of function spaces, especially of HölderZygmund type. We discuss
Gelfand numbers of embeddings of mixed Besov spaces
Sampling discretization error of integral norms for function classes
Optimization on Spaces of Curves


A φ-Transform Result for Spaces with Dominating Mixed Smoothness Properties
This note is concerned with spaces of functions possessing dominating mixed smoothness properties. In particular, it includes the proof of a φ-transform result for those function spaces of
A diagonal embedding theorem for function spaces with dominating mixed smoothness
The aim of this paper is to study the diagonal embeddings of function spaces with dominating mixed smoothness. From certain point of view, this paper may be considered as a direct continuation of [8]
Characterisations of function spaces with dominating mixed smoothness properties
We investigate function spaces with dominating mixed smoothness properties of Besov and Triebel-Lizorkin type. Equivalent quasi-norms in terms of local means are derived. Also theorems on atomic and
Function spaces with dominating mixed smoothness
We study several techniques whichare well known in the case of Besov and TriebelLizorkin spaces and extend them to spaces with dominating mixed smoothness. We use the ideas of Triebel to prove three
Measure and Integral
Mass und Integral und ihre AlgebraisierungVon Prof. C. Carathéodory. Herausgegeben von P. Finsler, A. Rosenthal und R. Steuerwald. (Lehrbücher und Monographien aus dem Gebiete der Exakten
Introduction to Fourier Analysis on Euclidean Spaces.
The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action
Topics in Fourier Analysis and Function Spaces
Preface Spaces of Entire Analytic Functions Spaces with Dominating Mixed Smoothness Properties Periodic Spaces Anisotropic Spaces Further Types of Function Spaces Abstract Spaces References Index.
On spaces of Triebel—Lizorkin type
In this note we study certain spaces of distributions F;q=Fpq(R ") where s real, 0 < p , q<--~. They are intimately related to certain spaces studied by Triebel [10] and Lizorkin [5] (cf. also [6])
The Banach envelopes of Besov and Triebel-Lizorkin spaces and applications to partial differential equations
With “hat” denoting the Banach envelope (of a quasi-Banach space) we prove that if 0<p<1, 0<q<1, ℝ, while if 0<p<1, 1≤q<+∞, ∝, and if 1≤p<+∞, 0<q<1, ℝ.Applications to questions regarding the global
Optimal Sobolev embeddings on Rn
We study Sobolev-type embeddings involving rearrangement-invariant norms. In particular, we focus on the question when such embeddings are optimal. We concentrate on the case when the functions