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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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.
M. Mateljević (1979)
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...
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.
A. Ramayyan (1994)
Kybernetika
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David M. Boyd (1978)
Colloquium Mathematicae
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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.
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...
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...
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 .
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.
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 ≤ ∞.
Kunyu Guo, Yongjiang Duan (2006)
Studia Mathematica
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Let M be a Beurling-type submodule of , the Hardy space over the unit ball of , and let be the associated quotient module. We completely describe the spectrum and essential spectrum of N, and related index theory.
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.
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...
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...
Oscar Blasco (1988)
Colloquium Mathematicae
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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...
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-.
Muhammad Arshad, Eskandar Ameer, Aftab Hussain (2015)
Archivum Mathematicum
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The aim of this paper is to introduce some new fixed point results of Hardy-Rogers-type for ---contraction in a complete metric space. We extend the concept of -contraction into an ---contraction of Hardy-Rogers-type. An example has been constructed to demonstrate the novelty of our results.
Tomas Ekholm, Rupert Frank (2008)
Journal of the European Mathematical Society
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We consider the operator in with Dirichlet boundary condition at the origin. For the moments of its negative eigenvalues we prove the bound for any and . This includes a Lieb-Thirring inequality in the critical endpoint case.
Ushangi Goginava (2008)
Studia Mathematica
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The main aim of this paper is to prove that the maximal operator is bounded from the Hardy space to weak- and is not bounded from to .
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 .
Eric Amar (2008)
Studia Mathematica
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Let A be a uniform algebra on X and σ a probability measure on X. We define the Hardy spaces and the interpolating sequences S in the p-spectrum of σ. We prove, under some structural hypotheses on A and σ, that if S is a “dual bounded” Carleson sequence, then S is -interpolating with a linear extension operator for s < p, provided that either p = ∞ or p ≤ 2. In the case of the unit ball of ℂⁿ we find, for instance, that if S is dual bounded in then S is -interpolating with...