Embeddings and entropy numbers in Besov spaces of generalized smoothness

2000 ◽  
pp. 345-358
Keyword(s):  
Besov Spaces ◽  
Entropy Numbers

Entropy numbers of embedding maps between Besov spaces with an application to eigenvalue problems

1981 ◽  
Vol 90 (1-2) ◽  
pp. 63-70 ◽  
Author(s):  
Bernd Carl
Keyword(s):  
Banach Space ◽  
Asymptotic Behaviour ◽  
Besov Spaces ◽  
Eigenvalue Problems ◽  
Function Spaces ◽  
Sequence Spaces ◽  
Entropy Numbers ◽  
Diagonal Operators

SynopsisIn this paper we determine the asymptotic behaviour of entropy numbers of embedding maps between Besov sequence spaces and Besov function spaces. The results extend those of M. Š. Birman, M. Z. Solomjak and H. Triebel originally formulated in the language of ε-entropy. It turns out that the characterization of embedding maps between Besov spaces by entropy numbers can be reduced to the characterization of certain diagonal operators by their entropy numbers.Finally, the entropy numbers are applied to the study of eigenvalues of operators acting on a Banach space which admit a factorization through embedding maps between Besov spaces.The statements of this paper are obtained by results recently proved elsewhere by the author.

Frame Characterizations of Besov and Triebel–Lizorkin Spaces on Spaces of Homogeneous Type and their Applications

2002 ◽  
Vol 9 (3) ◽  
pp. 567-590
Author(s):  
Dachun Yang
Keyword(s):  
Besov Spaces ◽  
Interpolation Method ◽  
Real Interpolation ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Entropy Numbers ◽  
Compact Embeddings

Abstract The author first establishes the frame characterizations of Besov and Triebel–Lizorkin spaces on spaces of homogeneous type. As applications, the author then obtains some estimates of entropy numbers for the compact embeddings between Besov spaces or between Triebel–Lizorkin spaces. Moreover, some real interpolation theorems on these spaces are also established by using these frame characterizations and the abstract interpolation method.

scholarly journals Entropy numbers of embeddings of some 2-microlocal Besov spaces

2011 ◽  
Vol 163 (4) ◽  
pp. 505-523 ◽  
Author(s):  
Hans-Gerd Leopold ◽  
Leszek Skrzypczak
Keyword(s):  
Besov Spaces ◽  
Entropy Numbers

Entropy numbers of embeddings of weighted Besov spaces III. Weights of logarithmic type

2006 ◽  
Vol 255 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Thomas Kühn ◽  
Hans-Gerd Leopold ◽  
Winfried Sickel ◽  
Leszek Skrzypczak
Keyword(s):  
Besov Spaces ◽  
Entropy Numbers ◽  
Weighted Besov Spaces ◽  
Logarithmic Type

scholarly journals !ENTROPY NUMBERS OF EMBEDDINGS OF WEIGHTED BESOV SPACES. II

2006 ◽  
Vol 49 (2) ◽  
pp. 331-359 ◽  
Author(s):  
Thomas Kühn ◽  
Hans-Gerd Leopold ◽  
Winfried Sickel ◽  
Leszek Skrzypczak
Keyword(s):  
Asymptotic Behaviour ◽  
Large Class ◽  
Besov Space ◽  
Besov Spaces ◽  
Compact Embedding ◽  
Entropy Numbers ◽  
Weighted Besov Spaces ◽  
Weighted Besov Space

AbstractWe investigate the asymptotic behaviour of the entropy numbers of the compact embedding $B^{s_1}_{p_1,q_1}(\mathbb{R}^d,w_1)\hookrightarrow B^{s_2}_{p_2,q_2}(\mathbb{R}^d,w_2)$. Here $B^s_{p,q}(\mathbb{R}^d,w)$ denotes a weighted Besov space. We present a general approach which allows us to work with a large class of weights.

scholarly journals Approximation and entropy numbers in Besov spaces of generalized smoothness

2009 ◽  
Vol 160 (1-2) ◽  
pp. 56-70 ◽  
Author(s):  
Fernando Cobos ◽  
Thomas Kühn
Keyword(s):  
Besov Spaces ◽  
Entropy Numbers

Operator ideals and the absolute convergence of Fourier series

2011 ◽  
Vol 48 (1) ◽  
pp. 104-115
Author(s):  
Manuel Fugarolas
Keyword(s):  
Fourier Series ◽  
Besov Spaces ◽  
Absolute Convergence ◽  
Operator Ideals ◽  
Entropy Numbers ◽  
Approximation Numbers ◽  
Convergent Fourier Series ◽  
The Absolute ◽  
Series Of Functions

In this paper we give some relationships between the absolutely convergent Fourier series of functions belonging to Besov spaces and their connection with the theory of operator ideals. In this context, we give results in operator ideals associated with generalized approximation numbers, Weyl numbers and entropy numbers.

Entropy Numbers of Embeddings of Weighted Besov Spaces

2005 ◽  
Vol 23 (1) ◽  
pp. 61-77 ◽  
Author(s):  
Thomas Kuhn ◽  
Hans-Gerd Leopold ◽  
Winfried Sickel ◽  
Leszek Skrzypczak
Keyword(s):  
Besov Spaces ◽  
Entropy Numbers ◽  
Weighted Besov Spaces
Sign in / Sign up

Export Citation Format

Share Document