scholarly journals Mixed norm spaces of analytic functions as spaces of generalized fractional derivatives of functions in Hardy type spaces

2017 ◽  
Vol 20 (5) ◽  
Author(s):  
Alexey Karapetyants ◽  
Stefan Samko
Keyword(s):  
Analytic Functions ◽  
Fractional Derivatives ◽  
Mixed Norm ◽  
Mixed Norm Spaces ◽  
Hardy Type ◽  
Type Spaces ◽  
Generalized Fractional Derivatives ◽  
Definition Of ◽  
Derivatives Of ◽  
Spaces Of Analytic Functions

AbstractThe aim of the paper is twofold. First, we present a new general approach to the definition of a class of mixed norm spaces of analytic functions 𝓐

scholarly journals Multipliers

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1277-1283 ◽  
Author(s):  
Miroljub Jevtic
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Mixed Norm ◽  
Bounded Analytic Functions ◽  
Mixed Norm Spaces ◽  
Spaces Of Analytic Functions

We describe the multiplier spaces (Hp,q,?,H?), and (Hp,q,?,H?,v,?), where Hp,q,? are mixed norm spaces of analytic functions in the unit disk D and H? is the space of bounded analytic functions in D. We extend some results from [7] and [3], particularly Theorem 4.3 in [3].

scholarly journals On an Integral-Type Operator from Zygmund-Type Spaces to Mixed-Norm Spaces on the Unit Ball

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Type Operator ◽  
Mixed Norm ◽  
Integral Type ◽  
Mixed Norm Space ◽  
Mixed Norm Spaces ◽  
Norm Space ◽  
Type Spaces

The boundedness and compactness of an integral-type operator recently introduced by the author from Zygmund-type spaces to the mixed-norm space on the unit ball are characterized here.

scholarly journals On M-ideals and o-O type spaces

2017 ◽  
Vol 121 (1) ◽  
pp. 151 ◽  
Author(s):  
Karl-Mikael Perfekt
Keyword(s):  
Banach Spaces ◽  
Analytic Functions ◽  
Function Spaces ◽  
Weighted Spaces ◽  
Bounded Mean Oscillation ◽  
Mean Oscillation ◽  
Type Spaces ◽  
Invariant Spaces ◽  
Holder Spaces ◽  
Spaces Of Analytic Functions

We consider pairs of Banach spaces $(M_0, M)$ such that $M_0$ is defined in terms of a little-$o$ condition, and $M$ is defined by the corresponding big-$O$ condition. The construction is general and pairs include function spaces of vanishing and bounded mean oscillation, vanishing weighted and weighted spaces of functions or their derivatives, Möbius invariant spaces of analytic functions, Lipschitz-Hölder spaces, etc. It has previously been shown that the bidual $M_0^{**}$ of $M_0$ is isometrically isomorphic with $M$. The main result of this paper is that $M_0$ is an M-ideal in $M$. This has several useful consequences: $M_0$ has Pełczýnskis properties (u) and (V), $M_0$ is proximinal in $M$, and $M_0^*$ is a strongly unique predual of $M$, while $M_0$ itself never is a strongly unique predual.

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