scholarly journals Embedding of Besov Spaces and the Volterra Integral Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Dan Qu ◽  
Xiangling Zhu ◽  
Ruishen Qian
Keyword(s):  
Integral Operator ◽  
Besov Spaces ◽  
Essential Norm ◽  
Function Spaces ◽  
General Function ◽  
Tent Spaces ◽  
Volterra Integral Operator ◽  
Inclusion Mapping

The boundedness and compactness of the inclusion mapping from Besov spaces to tent spaces are studied in this paper. Meanwhile, the boundedness, compactness, and essential norm of the Volterra integral operator T g from Besov spaces to a class of general function spaces are also investigated.

Embedding of Dirichlet type spaces into tent spaces and Volterra operators

2020 ◽  
pp. 1-12
Author(s):  
Ruishen Qian ◽  
Xiangling Zhu
Keyword(s):  
Integral Operators ◽  
Essential Norm ◽  
Function Spaces ◽  
General Function ◽  
Tent Spaces ◽  
Dirichlet Type ◽  
Volterra Operators ◽  
Type Spaces ◽  
Inclusion Mapping ◽  
Dirichlet Type Spaces

Abstract In this paper, we study the boundedness and compactness of the inclusion mapping from Dirichlet type spaces $\mathcal {D}^{p}_{p-1 }$ to tent spaces. Meanwhile, the boundedness, compactness, and essential norm of Volterra integral operators from Dirichlet type spaces $\mathcal {D}^{p}_{p-1 }$ to general function spaces are also investigated.

scholarly journals Norm of a Volterra Integral Operator on Some Analytic Function Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Hao Li ◽  
Songxiao Li
Keyword(s):  
Analytic Function ◽  
Integral Operator ◽  
Unit Disc ◽  
Function Spaces ◽  
Volterra Integral Operator ◽  
Analytic Function Spaces

Let f be an analytic function in the unit disc 𝔻. The Volterra integral operator If is defined as follows: If(h)(z)=∫0zf(w)h'(w)dw,h∈H(𝔻),z∈𝔻. In this paper, we compute the norm of If on some analytic function spaces.

scholarly journals Embedding of Qp spaces into tent spaces and Volterra integral operator

2021 ◽  
Vol 6 (1) ◽  
pp. 698-711
Author(s):  
Ruishen Qian ◽  
◽  
Xiangling Zhu ◽  
Keyword(s):  
Integral Operator ◽  
Tent Spaces ◽  
Volterra Integral Operator

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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