scholarly journals Fourier Multipliers between Weighted Anisotropic Function Spaces. Part I: Besov Spaces

1996 ◽  
Vol 15 (3) ◽  
pp. 579-601
Author(s):  
P. Dintelmann
Keyword(s):  
Besov Spaces ◽  
Function Spaces ◽  
Fourier Multipliers ◽  
Anisotropic Function

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.

scholarly journals Operator-valued Fourier multipliers on toroidal Besov spaces

2016 ◽  
Vol 50 (1) ◽  
pp. 109-137 ◽  
Author(s):  
Bienvenido Barraza Martínez ◽  
Iván González Martínez ◽  
Jairo Hernández Monzón
Keyword(s):  
Besov Spaces ◽  
Fourier Multipliers

scholarly journals Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces

2017 ◽  
Vol 5 (1) ◽  
pp. 98-115 ◽  
Author(s):  
Eero Saksman ◽  
Tomás Soto
Keyword(s):  
Sobolev Space ◽  
Sobolev Spaces ◽  
Metric Space ◽  
Besov Spaces ◽  
Metric Spaces ◽  
Function Spaces ◽  
First Order ◽  
Trace Theorems ◽  
Euclidean Setting ◽  
Regular Subset

Abstract We establish trace theorems for function spaces defined on general Ahlfors regular metric spaces Z. The results cover the Triebel-Lizorkin spaces and the Besov spaces for smoothness indices s < 1, as well as the first order Hajłasz-Sobolev space M1,p(Z). They generalize the classical results from the Euclidean setting, since the traces of these function spaces onto any closed Ahlfors regular subset F ⊂ Z are Besov spaces defined intrinsically on F. Our method employs the definitions of the function spaces via hyperbolic fillings of the underlying metric space.

scholarly journals Unimodular Fourier multipliers on homogeneous Besov spaces

2015 ◽  
Vol 425 (1) ◽  
pp. 536-547 ◽  
Author(s):  
Guoping Zhao ◽  
Jiecheng Chen ◽  
Dashan Fan ◽  
Weichao Guo
Keyword(s):  
Besov Spaces ◽  
Fourier Multipliers

scholarly journals Non-smooth atomic decompositions of anisotropic function spaces and some applications

2007 ◽  
Vol 180 (2) ◽  
pp. 169-190 ◽  
Author(s):  
Susana D. Moura ◽  
Iwona Piotrowska ◽  
Mariusz Piotrowski
Keyword(s):  
Function Spaces ◽  
Atomic Decompositions ◽  
Anisotropic Function
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