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Pascal Lefevre - One of the best experts on this subject based on the ideXlab platform.
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Compact composition operators on Bergman-Orlicz Spaces
Transactions of the American Mathematical Society, 2013Co-Authors: Pascal Lefevre, Herve Queffelec, Luis Rodríguez-piazzaAbstract:We construct an analytic self-map ' of the unit disk and an Orlicz functionfor which the composition operator of symbol ' is compact on the Hardy-Orlicz Space H � , but not on the Bergman-Orlicz Space B � . For that, we first prove a Carleson embedding theorem, and then characterize the compact- ness of composition operators on Bergman-Orlicz Spaces, in terms of Carleson function (of order 2). We show that this Carleson function is equivalent to the Nevanlinna counting function of order 2. Mathematics Subject Classification. Primary: 47B33 - Secondary: 30D50; 30D55; 46E15
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When strict singularity of operators coincides with weak compactness
Journal of Operator Theory, 2012Co-Authors: Pascal LefevreAbstract:We prove that the notions of finite strict singularity, strict singularity and weak compactness coincide for operators defined on various Spaces: the disc algebra, subSpaces of C(K) with reflexive annihilator and subSpaces of the Morse-Transue-Orlicz Space $M^{\psi_q} (\Omega;\mu )$ with q > 2.
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The canonical injection of the Hardy-Orlicz Space Hw into the Bergman-Orlicz Space Bw
Studia Mathematica, 2011Co-Authors: Pascal Lefevre, Herve Queffelec, Luis Rodríguez-piazzaAbstract:We study the canonical injection from the Hardy-Orlicz Space H � into the Bergman-Orlicz Space B � . Mathematics Subject Classification. Primary: 46E30 - Secondary: 30D55; 30H05; 32A35; 32A36; 42B30
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The canonical injection of the Hardy-Orlicz Space $H^\Psi$ into the Bergman-Orlicz Space ${\mathfrak B}^\Psi$
arXiv: Functional Analysis, 2010Co-Authors: Pascal Lefevre, Herve Queffelec, Luis Rodríguez-piazzaAbstract:We study the canonical injection from the Hardy-Orlicz Space $H^\Psi$ into the Bergman-Orlicz Space ${\mathfrak B}^\Psi$.
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Compact composition operators on Bergman-Orlicz Spaces
arXiv: Functional Analysis, 2009Co-Authors: Pascal Lefevre, Herve Queffelec, Luis Rodríguez-piazzaAbstract:We construct an analytic self-map $\phi$ of the unit disk and an Orlicz function $\Psi$ for which the composition operator of symbol $\phi$ is compact on the Hardy-Orlicz Space $H^\Psi$, but not compact on the Bergman-Orlicz Space ${\mathfrak B}^\Psi$. For that, we first prove a Carleson embedding theorem, and then characterize the compactness of composition operators on Bergman-Orlicz Spaces, in terms of Carleson function (of order 2). We show that this Carleson function is equivalent to the Nevanlinna counting function of order 2.
Yu-xia Liang - One of the best experts on this subject based on the ideXlab platform.
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new characterizations for differences of volterra type operators from α weighted type Space to β bloch Orlicz Space
Mathematische Nachrichten, 2018Co-Authors: Yu-xia Liang, Cui ChenAbstract:Firstly, we presented three equivalent characterizations for the boundedness of the difference of general Volterra‐type operators from α‐weighted‐type Space to β‐Bloch–Orlicz Space. Especially, the descriptions in terms of the n‐th power of the induced analytic self‐maps were described. And then we estimated their essential norms, which can provide new compactness criteria and be seen as generalizations of classical results. Finally, we completed this paper with similar results on the differences of other three integral‐type operators, which extend and strengthen several existing results in the literature.
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volterra type operators from weighted bergman Orlicz Space to beta zygmund Orlicz and gamma bloch Orlicz Spaces
Monatshefte für Mathematik, 2017Co-Authors: Yu-xia LiangAbstract:We find the conditions to ensure the boundedness and compactness of the Volterra-type operators acting from weighted Bergman–Orlicz Space to \(\beta \)-Zygmund–Orlicz and \(\gamma \)-Bloch–Orlicz Spaces, respectively.
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Volterra-type operators from weighted Bergman–Orlicz Space to \beta -Zygmund–Orlicz and \gamma -Bloch–Orlicz Spaces
Monatshefte für Mathematik, 2016Co-Authors: Yu-xia LiangAbstract:We find the conditions to ensure the boundedness and compactness of the Volterra-type operators acting from weighted Bergman–Orlicz Space to \(\beta \)-Zygmund–Orlicz and \(\gamma \)-Bloch–Orlicz Spaces, respectively.
Peter Hästö - One of the best experts on this subject based on the ideXlab platform.
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Statistical manifold as an affine Space: A functional equation approach
Journal of Mathematical Psychology, 2006Co-Authors: Jun Zhang, Peter HästöAbstract:Abstract A statistical manifold M μ consists of positive functions f such that f d μ defines a probability measure. In order to define an atlas on the manifold, it is viewed as an affine Space associated with a subSpace of the Orlicz Space L Φ . This leads to a functional equation whose solution, after imposing the linearity constrain in line with the vector Space assumption, gives rise to a general form of mappings between the affine probability manifold and the vector (Orlicz) Space. These results generalize the exponential statistical manifold and clarify some foundational issues in non-parametric information geometry.
Xiaolin Zeng - One of the best experts on this subject based on the ideXlab platform.
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On the Orlicz Space generated from a random normed module
arXiv: Functional Analysis, 2015Co-Authors: Long Long, Xiaolin ZengAbstract:In this paper, we first introduce the notion of the Orlicz Space generated from a random normed module $E$. Then we give a representation theorem which identify the dual of the Orlicz heart of $E$ with the Orlicz Space generated from the random conjugate Space of $E$. Finally, we establish relations between the strict convexity and uniform convexity of this Orlicz Space and the random strict convexity and random uniform convexity of the underlying random normed module, respectively.
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some results on the Orlicz Space generated from a random normed module
arXiv: Functional Analysis, 2015Co-Authors: Long Long, Xiaolin ZengAbstract:Noting the important role the abstract $L^p$ Space has played in the development of random normed modules, in this paper we introduce and study the Orlicz Space generated from a random normed module. First, we give a basic dual Space representation theorem which identify the dual of the Orlicz heart of a random normed module with the Orlicz Space generated from the random conjugate Space. Then, we establish the respective equivalence relations of the strict convexity and uniform convexity of this abstract Orlicz Space to the random strict convexity and random uniform convexity of the underlying random normed module. These results demonstrate that it is possible to use the Orlicz Space theory in the further development of random nomed modules.
M. L. Goldman - One of the best experts on this subject based on the ideXlab platform.
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weighted inequalities for hardy type operators on the cone of decreasing functions in an Orlicz Space
Mathematical Notes, 2017Co-Authors: E. G. Bakhtigareeva, M. L. GoldmanAbstract:We establish criteria for the validity of modular inequalities for the Hardy operator on the cone Ω of nonnegative decreasing functions from weighted Orlicz Spaces with general weight. The result is based on the theorem on the reduction of modular inequalities for positively homogeneous operators on the cone Ω, which enables passing to modular inequalities for modified operators on the cone of all nonnegative functions from an Orlicz Space. It is shown that, for the Hardy operator, the modified operator is a generalized Hardy operator. This enables us to establish explicit criteria for the validity of modular inequalities.
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Modular and norm inequalities for operators on the cone of decreasing functions in Orlicz Space
Doklady Mathematics, 2017Co-Authors: M. L. GoldmanAbstract:Modular and norm inequalities are considered for positively homogeneous operators on the cone of all nonnegative functions and on the cone Ω of nonnegative decreasing functions from the weighted Orlicz Space with a general weight and a general Young function. A reduction theorem is obtained for the norm of an operator on Ω. This norm is shown to be equivalent to the norm of a modified operator on the cone of all nonnegative functions in the above Orlicz Space. A similar theorem is obtained for modular inequalities. The results are based on the application of the principle of duality, which gives a description of the associated Orlicz norm for Ω. We also establish the equivalence of modular inequalities on the cone Ω and modified modular inequalities on the cone of all nonnegative functions in Orlicz Space. In the general situation, the forms of these answers are substantially different from the descriptions obtained earlier by P. Drabek, A. Kufner, and H. Heinig under the assumption that the Young function and its complementary function satisfy Δ_2-conditions.
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estimates for restrictions of monotone operators on the cone of decreasing functions in Orlicz Space
Mathematical Notes, 2016Co-Authors: M. L. GoldmanAbstract:The restriction of a monotone operator P to the cone Ω of nonnegative decreasing functions from a weighted Orlicz Space Lφ,v without additional a priori assumptions on the properties of theOrlicz function φ and the weight function v is considered. An order-sharp two-sided estimate of the norm of this restriction is established by using a specially constructed discretization procedure. Similar estimates are also obtained for monotone operators over the corresponding Orlicz–Lorentz Spaces Λφ,v. As applications, descriptions of associated Spaces for the cone Ω and the Orlicz–Lorentz Space are obtained. These new results are of current interest in the theory of such Spaces.