Compact composition operators on the Dirichlet space and capacity of sets of contact points [PDF]
, 2012 In this paper, we prove that for every compact set of the unit disk of logarithmic capacity 0, there exists a Schur function both in the disk algebra and in the Dirichlet space such that the associated composition operator is in all Schatten classes (of ...
Lefèvre, Pascal +3 more
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Sharp Bounds for Fractional Conjugate Hardy Operator on Higher-Dimensional Product Spaces
Journal of Function Spaces, 2020 In this paper, we obtain the sharp bound for fractional conjugate Hardy operator on higher-dimensional product spaces from L1ℝn1×⋯×ℝnm to the space wLQℝn1×⋯×ℝnm and Lpℝn1×⋯×ℝnm to the space Lqℝn1×⋯×ℝnm. More generally, the operator norm of the fractional
Zequn Wang +3 more
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Some new properties of composition operators associated with lens maps [PDF]
, 2012 We give examples of results on composition operators connected with lens maps. The first two concern the approximation numbers of those operators acting on the usual Hardy space $H^2$.
Lefèvre, Pascal +3 more
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Orthorecursive expansions generated by the Szego kernel [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2023 This article considers systems of subspaces of the Hardy space generated by the Szego kernel. The main result of the work is to establish the convergence of orthorecursive expansions with respect to the considered systems of subspaces.
Terekhin, Pavel A.
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Molecular Characterization of Hardy Spaces Associated with Twisted Convolution
Journal of Function Spaces, 2014 We give a molecular characterization of the Hardy space associated with twisted convolution. As an application, we prove the boundedness of the local Riesz transform on the Hardy space.
Jizheng Huang, Yu Liu
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A Characterization of Central BMO Space via the Commutator of Fractional Hardy Operator
Journal of Function Spaces, 2020 This paper is devoted in characterizing the central BMO ℝn space via the commutator of the fractional Hardy operator with rough kernel. Precisely, by a more explicit decomposition of the operator and the kernel function, we will show that if the symbol ...
Lei Zhang, Shaoguang Shi
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Hardy-Type Space Associated with an Infinite-Dimensional Unitary Matrix Group
Abstract and Applied Analysis, 2013 We investigate an orthogonal system of the homogenous Hilbert-Schmidt polynomials with respect to a probability measure which is invariant under the right action of an infinite-dimensional unitary matrix group.
Oleh Lopushansky
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Herz-Type Hardy Spaces Associated with Operators
Journal of Function Spaces, 2018 Suppose L is a nonnegative, self-adjoint differential operator. In this paper, we introduce the Herz-type Hardy spaces associated with operator L. Then, similar to the atomic and molecular decompositions of classical Herz-type Hardy spaces and the Hardy ...
Yan Chai, Yaoyao Han, Kai Zhao
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Certain properties of continuous fractional wavelet transform on Hardy space and Morrey space [PDF]
Opuscula Mathematica, 2021 In this paper we define a new class of continuous fractional wavelet transform (CFrWT) and study its properties in Hardy space and Morrey space. The theory developed generalize and complement some of already existing results.
Amit K. Verma, Bivek Gupta
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Geometric Hardy and Hardy–Sobolev inequalities on Heisenberg groups
Bulletin of Mathematical Sciences, 2020 In this paper, we present geometric Hardy inequalities for the sub-Laplacian in half-spaces of stratified groups. As a consequence, we obtain the following geometric Hardy inequality in a half-space of the Heisenberg group with a sharp constant: ∫ℍ ...
Michael Ruzhansky +2 more
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