Growth estimates for generalized factors of $H^{p}$ spaces

Joseph A. Cima; Angeliki Kazas; Michael I. Stessin

Displaying similar documents to “Growth estimates for generalized factors of $H^{p}$ spaces”

Factorization of sequences in discrete Hardy spaces

Santiago Boza (2012)

Studia Mathematica

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The purpose of this paper is to obtain a discrete version for the Hardy spaces $H^{p} (ℤ)$ of the weak factorization results obtained for the real Hardy spaces $H^{p} (ℝ ⁿ)$ by Coifman, Rochberg and Weiss for p > n/(n+1), and by Miyachi for p ≤ n/(n+1). It represents an extension, in the one-dimensional case, of the corresponding result by A. Uchiyama who obtained a factorization theorem in the general context of spaces X of homogeneous type, but with some restrictions on the measure that exclude the case...

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

M. Jevtić (1988)

Matematički Vesnik

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

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 $H_{u}^{p} (Ω)$ 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 $H_{u}^{p} (Ω)$ where the Monge-Ampère measure $(d d^{c} u) ⁿ$ has compact support for the associated...

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

Krzysztof Grelowski (2008)

Annales Polonici Mathematici

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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.

On $n$ th order differential equations over Hardy fields

A. Ramayyan (1994)

Kybernetika

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Notes on commutator on the variable exponent Lebesgue spaces

Dinghuai Wang (2019)

Czechoslovak Mathematical Journal

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

M. Mateljević (1979)

Matematički Vesnik

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$H^{p}$ Sobolev spaces

Robert S. Strichartz (1990)

Colloquium Mathematicae

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On weighted Hardy spaces on the unit disk

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 $H_{u}^{p}$ . 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.

Boundedness of the Hausdorff operators in $H^{p}$ spaces, 0 < p < 1

Elijah Liflyand, Akihiko Miyachi (2009)

Studia Mathematica

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Sufficient conditions for the boundedness of the Hausdorff operators in the Hardy spaces $H^{p}$ , 0 < p < 1, on the real line are proved. Two related negative results are also given.

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 $H^{p} (ℝ)$ .

On contractive projections in Hardy spaces

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, $H_{p} ()$ 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.

On the spectrum of the p-biharmonic operator involving p-Hardy's inequality

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: ${Δ (| Δ u |}^{p - 2} {Δ u) = λ (| u |}^{p - 2} u) / (δ {(x)}^{2 p})$ in Ω, $u \in W ₀^{2, p} (Ω)$ . 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.

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

David M. Boyd (1978)

Colloquium Mathematicae

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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...

A rigidity phenomenon for the Hardy-Littlewood maximal function

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 $f \in C^{α} (ℝ, ℝ)$ be a periodic function and α > 1/2. If there exists a real number 0 < γ < ∞ such that the averaging operator $(A_{x} f) (r) = 1 / 2 r \int_{x - r}^{x + r} f (z) d z$ 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...

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...

Doubly commuting submodules of the Hardy module over polydiscs

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 $H^{\infty} (ⁿ)$ .

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.

Weighted multi-parameter mixed Hardy spaces and their applications

Wei Ding, Yun Xu, Yueping Zhu (2022)

Czechoslovak Mathematical Journal

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Applying discrete Calderón’s identity, we study weighted multi-parameter mixed Hardy space $H_{mix}^{p} (ω, ℝ^{n_{1}} \times ℝ^{n_{2}})$ . Different from classical multi-parameter Hardy space, this space has characteristics of local Hardy space and Hardy space in different directions, respectively. As applications, we discuss the boundedness on $H_{mix}^{p} (ω, ℝ^{n_{1}} \times ℝ^{n_{2}})$ of operators in mixed Journé’s class.

Some Banach spaces of Dirichlet series

Maxime Bailleul, Pascal Lefèvre (2015)

Studia Mathematica

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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...

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 ≤ ∞.

On the dual space of $H_{B}^{1, \infty}$

Oscar Blasco (1988)

Colloquium Mathematicae

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Displaying similar documents to “Growth estimates for generalized factors of H p spaces”

Displaying similar documents to “Growth estimates for generalized factors of $H^{p}$ spaces”