An inclusion operator in Hardy spaces on the unit ball in
M. Jevtić (1988)
Matematički Vesnik
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M. Jevtić (1988)
Matematički Vesnik
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Sibel Şahin (2015)
Banach Center Publications
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Poletsky-Stessin Hardy (PS-Hardy) spaces are the natural generalizations of classical Hardy spaces of the unit disc to general bounded, hyperconvex domains. On a bounded hyperconvex domain Ω, the PS-Hardy space is generated by a continuous, negative, plurisubharmonic exhaustion function u of the domain. Poletsky and Stessin considered the general properties of these spaces and mainly concentrated on the spaces where the Monge-Ampère measure has compact support for the associated...
Krzysztof Grelowski (2008)
Annales Polonici Mathematici
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For a large class of Hardy fields their extensions containing non--germs are constructed. Hardy fields composed of only non--germs, apart from constants, are also considered.
Joseph A. Cima, Angeliki Kazas, Michael I. Stessin (2003)
Studia Mathematica
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With φ an inner function and the multiplication operator on a given Hardy space it is known that for any given function f in the Hardy space we may use the Wold decomposition to obtain a factorization of the given f (not the Riesz factorization). This new factorization has been shown to be useful in the study of commutants of Toeplitz operators. We study the smoothness of each factor of this factorization. We show in some cases that the factors lie in the same Hardy space (or smoothness...
A. Ramayyan (1994)
Kybernetika
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M. Mateljević (1979)
Matematički Vesnik
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Alberto Fiorenza, Babita Gupta, Pankaj Jain (2008)
Studia Mathematica
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We study the Hardy inequality and derive the maximal theorem of Hardy and Littlewood in the context of grand Lebesgue spaces, considered when the underlying measure space is the interval (0,1) ⊂ ℝ, and the maximal function is localized in (0,1). Moreover, we prove that the inequality holds with some c independent of f iff w belongs to the well known Muckenhoupt class , and therefore iff for some c independent of f. Some results of similar type are discussed for the case of small...
Evgeny A. Poletsky, Khim R. Shrestha (2015)
Banach Center Publications
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In this paper we completely characterize those weighted Hardy spaces that are Poletsky-Stessin Hardy spaces . We also provide a reduction of problems to problems and demonstrate how such a reduction can be used to make shortcuts in the proofs of the interpolation theorem and corona problem.
Jaydeb Sarkar, Amol Sasane, Brett D. Wick (2013)
Studia Mathematica
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In this note we establish a vector-valued version of Beurling’s theorem (the Lax-Halmos theorem) for the polydisc. As an application of the main result, we provide necessary and sufficient conditions for the “weak” completion problem in .
Abdelouahed El Khalil, My Driss Morchid Alaoui, Abdelfattah Touzani (2014)
Applicationes Mathematicae
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In this paper, we study the spectrum for the following eigenvalue problem with the p-biharmonic operator involving the Hardy term: in Ω, . By using the variational technique and the Hardy-Rellich inequality, we prove that the above problem has at least one increasing sequence of positive eigenvalues.
Florence Lancien, Beata Randrianantoanina, Eric Ricard (2005)
Studia Mathematica
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We prove a conjecture of Wojtaszczyk that for 1 ≤ p < ∞, p ≠ 2, does not admit any norm one projections with dimension of the range finite and greater than 1. This implies in particular that for 1 ≤ p < ∞, p ≠ 2, does not admit a Schauder basis with constant one.
Elijah Liflyand, Akihiko Miyachi (2009)
Studia Mathematica
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Sufficient conditions for the boundedness of the Hausdorff operators in the Hardy spaces , 0 < p < 1, on the real line are proved. Two related negative results are also given.
Stefan Steinerberger (2015)
Studia Mathematica
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The Hardy-Littlewood maximal function ℳ and the trigonometric function sin x are two central objects in harmonic analysis. We prove that ℳ characterizes sin x in the following way: Let be a periodic function and α > 1/2. If there exists a real number 0 < γ < ∞ such that the averaging operator has a critical point at r = γ for every x ∈ ℝ, then f(x) = a + bsin(cx+d) for some a,b,c,d ∈ ℝ. This statement can be used to derive a characterization of trigonometric functions as...
Yuichi Kanjin (2001)
Studia Mathematica
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We prove that the Hausdorff operator generated by a function ϕ is bounded on the real Hardy space , 0 < p ≤ 1, if the Fourier transform ϕ̂ of ϕ satisfies certain smoothness conditions. As a special case, we obtain the boundedness of the Cesàro operator of order α on , 2/(2α+1) < p ≤ 1. Our proof is based on the atomic decomposition and molecular characterization of .
David M. Boyd (1978)
Colloquium Mathematicae
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Maxime Bailleul, Pascal Lefèvre (2015)
Studia Mathematica
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The Hardy spaces of Dirichlet series, denoted by (p ≥ 1), have been studied by Hedenmalm et al. (1997) when p = 2 and by Bayart (2002) in the general case. In this paper we study some -generalizations of spaces of Dirichlet series, particularly two families of Bergman spaces, denoted and . Each could appear as a “natural” way to generalize the classical case of the unit disk. We recover classical properties of spaces of analytic functions: boundedness of point evaluation, embeddings...
R. Demazeux (2011)
Studia Mathematica
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We complete the different cases remaining in the estimation of the essential norm of a weighted composition operator acting between the Hardy spaces and for 1 ≤ p,q ≤ ∞. In particular we give some estimates for the cases 1 = p ≤ q ≤ ∞ and 1 ≤ q < p ≤ ∞.
Guanghui Lu, Shuangping Tao (2017)
Open Mathematics
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The main purpose of this paper is to prove that the boundedness of the commutator [...] Mκ,b∗ generated by the Littlewood-Paley operator [...] Mκ∗ and RBMO (μ) function on non-homogeneous metric measure spaces satisfying the upper doubling and the geometrically doubling conditions. Under the assumption that the kernel of [...] Mκ∗ satisfies a certain Hörmander-type condition, the authors prove that [...] Mκ,b∗ is bounded on Lebesgue spaces Lp(μ) for 1 < p < ∞, bounded from...
Oscar Blasco (1988)
Colloquium Mathematicae
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C. J. Neugebauer (2009)
Studia Mathematica
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Let be the Ariõ-Muckenhoupt weight class which controls the weighted -norm inequalities for the Hardy operator on non-increasing functions. We replace the constant p by a function p(x) and examine the associated -norm inequalities of the Hardy operator.
J. Alvarez (1989)
Colloquium Mathematicae
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István Blahota, György Gát, Ushangi Goginava (2007)
Colloquium Mathematicae
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The main aim of this paper is to prove that the maximal operator of the Fejér means of the double Vilenkin-Fourier series is not bounded from the Hardy space to the space weak-.
Leonardo Pasini (1985)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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In questo lavoro si estende il concetto di campo di Hardy [Bou], al contesto dei germi di funzioni in più variabili che sono definite su insiemi semi-algebrici [Br.], [D.] e che risultano essere morfismi di categorie lisce [Pal.]. In tale contesto si dimostra che per ogni campo di Hardy di germi di una fissata categoria liscia , la sua chiusura algebrica relativa nell'anello , di tutti i germi nella stessa categoria liscia, è un campo di Hardy reale chiuso, che è l'unica chiusura reale...
Ferenc Weisz (2009)
Studia Mathematica
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It is proved that the multi-dimensional maximal Fejér operator defined in a cone is bounded from the amalgam Hardy space to . This implies the almost everywhere convergence of the Fejér means in a cone for all , which is larger than .
A. de la Torre, J. L. Torrea (2003)
Studia Mathematica
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Let f be a measurable function defined on ℝ. For each n ∈ ℤ we consider the average . The square function is defined as . The local version of this operator, namely the operator , is of interest in ergodic theory and it has been extensively studied. In particular it has been proved [3] that it is of weak type (1,1), maps into itself (p > 1) and into BMO. We prove that the operator S not only maps into BMO but it also maps BMO into BMO. We also prove that the boundedness...
Michalak Artur
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AbstractThe paper contains studies of relationships between properties of the “translation” mappings and the topological and geometric structure of spaces X and Hardy classes of X-valued harmonic functions on the open unit disk in ℂ (X is a Banach space). The mapping transforming the unit circle of ℂ into is associated with a function by the formula , where ϕₜ is the rotation of through t.AcknowledgmentsThis work is based in part on the author’s doctoral thesis written at...
Ming-Yi Lee, Chin-Cheng Lin, Ying-Chieh Lin (2010)
Studia Mathematica
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We first show that a linear operator which is bounded on with w ∈ A₁ can be extended to a bounded operator on the weighted local Hardy space if and only if this operator is uniformly bounded on all -atoms. As an application, we show that every pseudo-differential operator of order zero has a bounded extension to .
Zhixin Liu, Shanzhen Lu (1993)
Studia Mathematica
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The aim of this paper is to establish transference and restriction theorems for maximal operators defined by multipliers on the Hardy spaces and , 0 < p ≤ 1, which generalize the results of Kenig-Tomas for the case p > 1. We prove that under a mild regulation condition, an function m is a maximal multiplier on if and only if it is a maximal multiplier on . As an application, the restriction of maximal multipliers to lower dimensional Hardy spaces is considered. ...
Leonardo Pasini (1985)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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In questo lavoro si estende il concetto di campo di Hardy [Bou], al contesto dei germi di funzioni in più variabili che sono definite su insiemi semi-algebrici [Br.], [D.] e che risultano essere morfismi di categorie lisce [Pal.]. In tale contesto si dimostra che per ogni campo di Hardy di germi di una fissata categoria liscia , la sua chiusura algebrica relativa nell'anello , di tutti i germi nella stessa categoria liscia, è un campo di Hardy reale chiuso, che è l'unica chiusura reale...