scholarly journals Characterization of BMO via ball Banach function spaces

2017 ◽  
Vol 4(62) (1) ◽  
pp. 78-86
Author(s):  
Izuki Mitsuo ◽  
◽  
Sawano Yoshihiro ◽  
Keyword(s):  
Function Spaces ◽  
Banach Function Spaces

scholarly journals Composition operators on some holomorphic Banach function spaces

2009 ◽  
Vol 104 (2) ◽  
pp. 275 ◽  
Author(s):  
A. El-Sayed Ahmed ◽  
M.A. Bakhit
Keyword(s):  
Composition Operator ◽  
Carleson Measure ◽  
Composition Operators ◽  
Bloch Space ◽  
Function Spaces ◽  
Banach Function Spaces

In this paper, we study composition operators on some Möbius invariant Banach function spaces like Bloch and $F(p,q,s)$ spaces. We give a Carleson measure characterization on $F(p,q,s)$ spaces, then we use this Carleson measure characterization of the compact compositions on $F(p,q,s)$ spaces to show that every compact composition operator on $F(p,q,s)$ spaces is compact on a Bloch space. Also, we give conditions to clarify when the converse holds.

scholarly journals The John–Nirenberg inequality in ball Banach function spaces and application to characterization of BMO

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Mitsuo Izuki ◽  
Takahiro Noi ◽  
Yoshihiro Sawano
Keyword(s):  
Maximal Operator ◽  
Function Spaces ◽  
Bounded Mean Oscillation ◽  
Banach Function Spaces ◽  
Mean Oscillation ◽  
Nirenberg Inequality ◽  
Associate Space ◽  
Littlewood Maximal Operator

Abstract Our goal is to obtain the John–Nirenberg inequality for ball Banach function spaces X, provided that the Hardy–Littlewood maximal operator M is bounded on the associate space $X'$ X ′ by using the extrapolation. As an application we characterize BMO, the bounded mean oscillation, via the norm of X.

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.

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