12 papers
Hölder Inequalities for Besov-Morrey and Triebel-Lizorkin-Morrey Spaces
Marc Hovemann
In this paper we prove Hölder inequalities for the Besov-Morrey spaces and the Triebel-Lizorkin-Morrey spaces $ \mathcal{E}^{s}_{u,p,q}(…
On the boundedness of dilation operators in the context of Triebel-Lizorkin-Morrey spaces
Marc Hovemann, Markus Weimar
In this paper we study the behavior of dilation operators with in the context of Triebel-Lizorkin-Morrey spaces $\mathcal{E}^{s}_{u,p,q…
Adaptive Bivariate Quarklet Tree Approximation via Anisotropic Tensor Quarklets
Marc Hovemann
This paper deals with near-best approximation of a given bivariate function using elements of quarkonial tensor frames. For that purpose we apply anisotropic tensor products of the…
Oscillations and differences in Besov-Morrey and Besov-type spaces
Marc Hovemann, Markus Weimar
In this paper we investigate Besov-Morrey spaces and Besov-type spaces of positive smoothness defined on Lipschitz domains $Ω\subset…
Quarklet Characterizations for bivariate Bessel-Potential Spaces on the Unit Square via Tensor Products
Marc Hovemann
In this paper we deduce new characterizations for bivariate Bessel-Potential spaces defined on the unit square via B-spline quarklets. For that purpose in a first step we use univa…
Oscillations and differences in Triebel-Lizorkin-Morrey spaces
Marc Hovemann, Markus Weimar
In this paper we are concerned with Triebel-Lizorkin-Morrey spaces of positive smoothness defined on (special or bounded) Lipschitz domains $Ω\subs…
Adaptive Quarklet Tree Approximation
Stephan Dahlke, Marc Hovemann, Thorsten Raasch +1
This paper is concerned with near-optimal approximation of a given function with elements of a polynomially enriched wavelet frame, a so-called quarklet frame. I…
B-Spline Quarklets and Biorthogonal Multiwavelets
Marc Hovemann, Anne Kopsch, Thorsten Raasch +1
We show that B-spline quarks and the associated quarklets fit into the theory of biorthogonal multiwavelets. Quark vectors are used to define sequences of subspaces of…
Quarklet Characterizations for Triebel-Lizorkin Spaces
Marc Hovemann, Stephan Dahlke
In this paper we prove that under some conditions on the parameters the one-dimensional Triebel-Lizorkin spaces can be described in terms of quarklets.…
Besov-Morrey spaces and differences (extended version)
Marc Hovemann
We study the Besov-Morrey spaces and show that under certain conditions on the parameters these spaces can be characterized in terms of…
Truncation in Besov-Morrey and Triebel-Lizorkin-Morrey spaces
Marc Hovemann
We will prove that under certain conditions on the parameters the operators and are bounded mappings on the Triebel-Lizorkin-Morrey and Besov-Morr…
Complex Interpolation of Lizorkin-Triebel-Morrey Spaces on Domains
Ciqiang Zhuo, Marc Hovemann, Winfried Sickel
In this article the authors study complex interpolation of Sobolev-Morrey spaces and their generalizations, Lizorkin-Triebel-Morrey spaces. Both scales are considered on bounded do…