Wavelet bases and entropy numbers in weighted function spaces

2005 ◽  
Vol 278 (1-2) ◽  
pp. 108-132 ◽  
Author(s):  
Dorothee D. Haroske ◽  
Hans Triebel
Keyword(s):  
Function Spaces ◽  
Entropy Numbers ◽  
Wavelet Bases ◽  
Weighted Function ◽  
Weighted Function Spaces

scholarly journals Nuclear Embeddings in Weighted Function Spaces

2020 ◽  
Vol 92 (6) ◽  
Author(s):  
Dorothee D. Haroske ◽  
Leszek Skrzypczak
Keyword(s):  
Function Spaces ◽  
Operator Ideal ◽  
Weighted Spaces ◽  
Wavelet Bases ◽  
Weighted Function ◽  
Weighted Function Spaces ◽  
Diagonal Operators ◽  
Polynomial Type ◽  
Muckenhoupt Class

AbstractWe study nuclear embeddings for weighted spaces of Besov and Triebel–Lizorkin type where the weight belongs to some Muckenhoupt class and is essentially of polynomial type. Here we can extend our previous results concerning the compactness of corresponding embeddings. The concept of nuclearity was introduced by A. Grothendieck in 1955. Recently there is a refreshed interest to study such questions. This led us to the investigation in the weighted setting. We obtain complete characterisations for the nuclearity of the corresponding embedding. Essential tools are a discretisation in terms of wavelet bases, operator ideal techniques, as well as a very useful result of Tong about the nuclearity of diagonal operators acting in $$\ell _p$$ ℓ p spaces. In that way we can further contribute to the characterisation of nuclear embeddings of function spaces on domains.

scholarly journals Linear Differential Equations on Some Classes of Weighted Function Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1113
Author(s):  
Ahmed El-Sayed Ahmed ◽  
Amnah E. Shammaky
Keyword(s):  
Specific Growth ◽  
Function Spaces ◽  
Entire Solutions ◽  
Linear Type ◽  
Weighted Function ◽  
Weighted Function Spaces ◽  
Type Classes ◽  
Type Differential Equation ◽  
Linear Differential ◽  
Weighted Type

Some weighted-type classes of holomorphic function spaces were introduced in the current study. Moreover, as an application of the new defined classes, the specific growth of certain entire-solutions of a linear-type differential equation by the use of concerned coefficients of certain analytic-type functions, that is the equation h(k)+Kk−1(υ)h(k−1)+…+K1(υ)h′+K0(υ)h=0, will be discussed in this current research, whereas the considered coefficients K0(υ),…,Kk−1(υ) are holomorphic in the disc ΓR={υ∈C:|υ|<R},0<R≤∞. In addition, some non-trivial specific examples are illustrated to clear the roles of the obtained results with some sharpness sense. Hence, the obtained results are strengthen to some previous interesting results from the literature.

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