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Hardy spaces meet harmonic weights
Transactions of the American Mathematical Society, 2022 We investigate the Hardy space H L 1 H^1_L associated with a self-adjoint operator L L defined in a general setting by Hofmann, Lu, Mitrea, Mitrea, and Yan [Mem. Amer. Math. Soc. 214 (2011), pp. vi+78]. We assume that there exists an L L -harmonic non-negative function
Preisner, Marcin +2 more
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Numerical Range on Weighted Hardy Spaces as Semi Inner Product Spaces
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017 The semi-inner product, in the sense of Lumer, on weighted Hardy space which generate the norm is unique. Also we will discuss some properties of the numerical range of bounded linear operators on weighted Hardy spaces.
Heydari Mohammad Taghi
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Sobolev–Hardy space with general weight
Journal of Mathematical Analysis and Applications, 2006 In this paper, the authors prove the following \(k\)th order Hardy inequality with general weight. Let \(\Omega\) be a bounded domain. Then, under the assumptions \((H_1)\) and \((H_2)\), for each positive integer \(k\) the inequality \[ \int_{\Omega}\phi|\nabla u|^2\,dx-\int_{\Omega}\phi\sum_{i=1}^{k}\left(\frac{h_i'}{h_i}\right)^2u^2\,dx\geq\int_ ...
Shen, Yaotian, Chen, Zhihui
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Abstract and Applied Analysis, 2010 The boundedness and compactness of weighted iterated radial composition operators from the mixed-norm space to the weighted-type space and the little weighted-type space on the unit ball are characterized here.
Stevo Stević
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Weighted Composition Operators on Hardy Spaces
Journal of Mathematical Analysis and Applications, 2001 This paper studies operators of the form \(f\mapsto (f\circ\varphi)\psi\) acting on Hardy spaces \(H^p\) of the unit disk \(D\), where \(\psi\) is analytic in \(D\) and \(\varphi\) is an analytic self-map of \(D\). Problems studied include the boundedness, compactness, weak compactness, and complete continuity of such operators.
Contreras, Manuel D +1 more
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Weighted composition operators from weighted hardy spaces to weighted-type spaces [PDF]
Demonstratio Mathematica, 2013 Abstract The boundedness and compactness of the weighted composition operator from weighted Hardy spaces to weighted-type spaces are studied in this paper.
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Abstract and Applied Analysis, 2013 The authors prove that the parametrized area integral and function are bounded from the weighted weak Hardy space to the weighted weak Lebesgue space as satisfies a class of the integral Dini condition, respectively.
Ximei Wei, Shuangping Tao
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GENERALIZED HARDY–CESÀRO OPERATORS BETWEEN WEIGHTED SPACES [PDF]
Glasgow Mathematical Journal, 2018 AbstractWe characterize those non-negative, measurable functions ψ on [0, 1] and positive, continuous functions ω1 and ω2 on ℝ+ for which the generalized Hardy–Cesàro operator $$\begin{equation*}(U_{\psi}f)(x)=\int_0^1 f(tx)\psi(t)\,dt\end{equation*}$$ defines a bounded operator Uψ: L1(ω1) → L1(ω2) This generalizes a result of Xiao [7] to weighted ...
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Hilbert-Schmidtness of weighted composition operators and their differences on Hardy spaces [PDF]
Opuscula Mathematica, 2020 Let \(u\) and \(\varphi\) be two analytic functions on the unit disk \(\mathbb{D}\) such that \(\varphi(\mathbb{D}) \subset \mathbb{D}\). A weighted composition operator \(uC_{\varphi}\) induced by \(u\) and \(\varphi\) is defined on \(H^2\), the Hardy ...
Ching-on Lo, Anthony Wai-keung Loh
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Antinormal Weighted Composition Operators
Abstract and Applied Analysis, 2016 Let l2=L2N,μ, where N is set of all positive integers and μ is the counting measure whose σ-algebra is the power set of N. In this paper, we obtain necessary and sufficient conditions for a weighted composition operator to be antinormal on the Hilbert ...
Dilip Kumar, Harish Chandra
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