Monge-Ampère measures and Poletsky-Stessin Hardy spaces on bounded hyperconvex domains

Sibel Şahin

Displaying similar documents to “Monge-Ampère measures and Poletsky-Stessin Hardy spaces on bounded hyperconvex domains”

An inclusion operator in Hardy spaces on the unit ball in $C^{N}$

M. Jevtić (1988)

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The isoperimetric inequality in the Hardy class $H^{1}$

M. Mateljević (1979)

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Extending Hardy fields by non- $^{\infty}$ -germs

Krzysztof Grelowski (2008)

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For a large class of Hardy fields their extensions containing non- $^{\infty}$ -germs are constructed. Hardy fields composed of only non- $^{\infty}$ -germs, apart from constants, are also considered.

Some Banach spaces of Dirichlet series

Maxime Bailleul, Pascal Lefèvre (2015)

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The Hardy spaces of Dirichlet series, denoted by $^{p}$ (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 $L^{p}$ -generalizations of spaces of Dirichlet series, particularly two families of Bergman spaces, denoted $^{p}$ and $ℬ^{p}$ . 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...

On weighted Hardy spaces on the unit disk

Evgeny A. Poletsky, Khim R. Shrestha (2015)

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In this paper we completely characterize those weighted Hardy spaces that are Poletsky-Stessin Hardy spaces $H_{u}^{p}$ . We also provide a reduction of $H^{\infty}$ problems to $H_{u}^{p}$ problems and demonstrate how such a reduction can be used to make shortcuts in the proofs of the interpolation theorem and corona problem.

On contractive projections in Hardy spaces

Florence Lancien, Beata Randrianantoanina, Eric Ricard (2005)

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We prove a conjecture of Wojtaszczyk that for 1 ≤ p < ∞, p ≠ 2, $H_{p} ()$ 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, $H_{p}$ does not admit a Schauder basis with constant one.

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A. Ramayyan (1994)

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The maximal theorem for weighted grand Lebesgue spaces

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 ${| | M f | |}_{p), w} {\leq c | | f | |}_{p), w}$ holds with some c independent of f iff w belongs to the well known Muckenhoupt class $A_{p}$ , and therefore iff ${| | M f | |}_{p, w} {\leq c | | f | |}_{p, w}$ for some c independent of f. Some results of similar type are discussed for the case of small...

The metric space $H^{p} (A)$ , 0

David M. Boyd (1978)

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Notes on commutator on the variable exponent Lebesgue spaces

Dinghuai Wang (2019)

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We obtain the factorization theorem for Hardy space via the variable exponent Lebesgue spaces. As an application, it is proved that if the commutator of Coifman, Rochberg and Weiss $[b, T]$ is bounded on the variable exponent Lebesgue spaces, then $b$ is a bounded mean oscillation (BMO) function.

The Hausdorff operators on the real Hardy spaces $H^{p} (ℝ)$

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 $H^{p} (ℝ)$ , 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 $H^{p} (ℝ)$ , 2/(2α+1) < p ≤ 1. Our proof is based on the atomic decomposition and molecular characterization of $H^{p} (ℝ)$ .

Essential norms of weighted composition operators between Hardy spaces $H^{p}$ and $H^{q}$ for 1 ≤ p,q ≤ ∞

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 $H^{p}$ and $H^{q}$ for 1 ≤ p,q ≤ ∞. In particular we give some estimates for the cases 1 = p ≤ q ≤ ∞ and 1 ≤ q < p ≤ ∞.

Boundedness of Littlewood-Paley operators relative to non-isotropic dilations

Shuichi Sato (2019)

Czechoslovak Mathematical Journal

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We consider Littlewood-Paley functions associated with a non-isotropic dilation group on $ℝ^{n}$ . We prove that certain Littlewood-Paley functions defined by kernels with no regularity concerning smoothness are bounded on weighted $L^{p}$ spaces, $1 < p < \infty$ , with weights of the Muckenhoupt class. This, in particular, generalizes a result of N. Rivière (1971).

A remark on the $H^{1}$ -BMO duality in product domains

J. Alvarez (1989)

Colloquium Mathematicae

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Weighted variable $L^{p}$ integral inequalities for the maximal operator on non-increasing functions

C. J. Neugebauer (2009)

Studia Mathematica

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Let $B_{p}$ be the Ariõ-Muckenhoupt weight class which controls the weighted $L^{p}$ -norm inequalities for the Hardy operator on non-increasing functions. We replace the constant p by a function p(x) and examine the associated $L^{p (x)}$ -norm inequalities of the Hardy operator.

Hardy fields in several variables

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 $\mathcal{C}$ , la sua chiusura algebrica relativa nell'anello $G\,\mathcal{C}$ , di tutti i germi nella stessa categoria liscia, è un campo di Hardy reale chiuso, che è l'unica chiusura reale...

Hardy fields in several variables

Leonardo Pasini (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Generalized Hardy spaces on tube domains over cones

Gustavo Garrigos (2001)

Colloquium Mathematicae

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We define a class of spaces $H_{μ}^{p}$ , 0 < p < ∞, of holomorphic functions on the tube, with a norm of Hardy type: ${| | F | |}_{H_{μ}^{p}}^{p} = s u p_{y \in Ω} \int_{Ω ̅} \int_{ℝ ⁿ} {| F (x + i (y + t)) |}^{p} d x d μ (t)$ . We allow μ to be any quasi-invariant measure with respect to a group acting simply transitively on the cone. We show the existence of boundary limits for functions in $H_{μ}^{p}$ , and when p ≥ 1, characterize the boundary values as the functions in $L_{μ}^{p}$ satisfying the tangential CR equations. A careful description of the measures μ when their supports lie on the boundary of the cone...

Translations of functions iv vector Hardy classes on the unit disk

Michalak Artur

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AbstractThe paper contains studies of relationships between properties of the “translation” mappings $T_{F}$ and the topological and geometric structure of spaces X and Hardy classes $h^{p} (, X)$ of X-valued harmonic functions on the open unit disk in ℂ (X is a Banach space). The mapping $T_{F}$ transforming the unit circle of ℂ into $h^{p} (, X)$ is associated with a function $F \in h^{p} (, X)$ by the formula $T_{F} (t) = F \circ ϕ ₜ$ , where ϕₜ is the rotation of through t.AcknowledgmentsThis work is based in part on the author’s doctoral thesis written at...

Maximal operators of Fejér means of double Vilenkin-Fourier series

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 $σ ₀ * : = s u p ₙ | σ_{n, n} |$ of the Fejér means of the double Vilenkin-Fourier series is not bounded from the Hardy space $H_{1 / 2}$ to the space weak- $L_{1 / 2}$ .

The John-Nirenberg inequality for functions of bounded mean oscillation with bounded negative part

Min Hu, Dinghuai Wang (2022)

Czechoslovak Mathematical Journal

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A version of the John-Nirenberg inequality suitable for the functions $b \in BMO$ with $b^{-} \in L^{\infty}$ is established. Then, equivalent definitions of this space via the norm of weighted Lebesgue space are given. As an application, some characterizations of this function space are given by the weighted boundedness of the commutator with the Hardy-Littlewood maximal operator.

Commutators of Littlewood-Paley [...] g κ ∗ $g_{κ}^{*}$ -functions on non-homogeneous metric measure spaces

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∗ $ℳ_{κ, b}^{*}$ generated by the Littlewood-Paley operator [...] Mκ∗ $ℳ_{κ}^{*}$ 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∗ $ℳ_{κ}^{*}$ satisfies a certain Hörmander-type condition, the authors prove that [...] Mκ,b∗ $ℳ_{κ, b}^{*}$ is bounded on Lebesgue spaces Lp(μ) for 1 < p < ∞, bounded from...