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1
Content available remote

Invertible and normal composition operators on the Hilbert Hardy space of a half–plane

100%
Matache V.
Concrete Operators
|
2016
|
tom 3
|
nr 1
77-84
EN
Operators on function spaces of form Cɸf = f ∘ ɸ, where ɸ is a fixed map are called composition operators with symbol ɸ. We study such operators acting on the Hilbert Hardy space over the right half-plane and characterize the situations when they are invertible, Fredholm, unitary, and Hermitian. We determine the normal composition operators with inner, respectively with Möbius symbol. In select cases, we calculate their spectra, essential spectra, and numerical ranges.
2
Content available remote

On some radius results for normalized analytic functions

100%
Kim Y., Kwon E.
Annales Polonici Mathematici
|
1998
|
tom 68
|
nr 1
51-60
EN
We investigate some radius results for various geometric properties concerning some subclasses of the class 𝓢 of univalent functions.
3
Content available remote

New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space

88%
Colonna F.
Open Mathematics
|
2013
|
tom 11
|
nr 1
55-73
EN
Let ψ and φ be analytic functions on the open unit disk $\mathbb{D}$ with φ($\mathbb{D}$) ⊆ $\mathbb{D}$. We give new characterizations of the bounded and compact weighted composition operators W ψ,ϕ from the Hardy spaces H p, 1 ≤ p ≤ ∞, the Bloch space B, the weighted Bergman spaces A αp, α > − 1,1 ≤ p < ∞, and the Dirichlet space $\mathcal{D}$ to the Bloch space in terms of boundedness (respectively, convergence to 0) of the Bloch norms of W ψ,ϕ f for suitable collections of functions f in the respective spaces. We also obtain characterizations of boundedness for H 1 as well as of compactness for H p, 1 ≤ p < ∞, and $\mathcal{D}$ purely in terms of the symbols ψ and φ.
4
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A natural localization of Hardy spaces in several complex variables

88%
Putinar M., Wolff R.
Annales Polonici Mathematici
|
1997
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tom 66
|
nr 1
183-201
EN
Let H²(bΩ) be the Hardy space of a bounded weakly pseudoconvex domain in $ℂ^n$. The natural resolution of this space, provided by the tangential Cauchy-Riemann complex, is used to show that H²(bΩ) has the important localization property known as Bishop's property (β). The paper is accompanied by some applications, previously known only for Bergman spaces.
5
Content available remote

Approximation numbers of composition operators on Hp

88%
Li D., Queffélec H., Rodríguez-Piazza L.
Concrete Operators
|
2015
|
tom 2
|
nr 1
EN
give estimates for the approximation numbers of composition operators on the Hp spaces, 1 ≤ p < ∞
6
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Commutators of Littlewood-Paley [...] g κ ∗ $g_{\kappa}^{*} $ -functions on non-homogeneous metric measure spaces

88%
Lu G., Tao S.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1283-1299
EN
The main purpose of this paper is to prove that the boundedness of the commutator [...] Mκ,b∗ $\mathcal{M}_{\kappa,b}^{*} $ generated by the Littlewood-Paley operator [...] Mκ∗ $\mathcal{M}_{\kappa}^{*} $ 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∗ $\mathcal{M}_{\kappa}^{*} $ satisfies a certain Hörmander-type condition, the authors prove that [...] Mκ,b∗ $\mathcal{M}_{\kappa,b}^{*} $ is bounded on Lebesgue spaces Lp(μ) for 1 < p < ∞, bounded from the space L log L(μ) to the weak Lebesgue space L1,∞(μ), and is bounded from the atomic Hardy spaces H1(μ) to the weak Lebesgue spaces L1,∞(μ).
7
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Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications

88%
Chen X., Jiang R., Yang D.
Analysis and Geometry in Metric Spaces
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2016
|
tom 4
|
nr 1
EN
Let Ω ⊂ Rn be a strongly Lipschitz domain. In this article, the authors study Hardy spaces, Hpr (Ω)and Hpz (Ω), and Hardy-Sobolev spaces, H1,pr (Ω) and H1,pz,0 (Ω) on , for p ∈ ( n/n+1, 1]. The authors establish grand maximal function characterizations of these spaces. As applications, the authors obtain some div-curl lemmas in these settings and, when is a bounded Lipschitz domain, the authors prove that the divergence equation div u = f for f ∈ Hpz (Ω) is solvable in H1,pz,0 (Ω) with suitable regularity estimates.
8
Content available remote

Some non-homogeneous Hardy spaces on locally compact Vilenkin groups

75%
Lu S., Yang D.
Colloquium Mathematicum
|
1996
|
tom 69
|
nr 1
1-17
9
Content available remote

Walsh-Marcinkiewicz means and Hardy spaces

75%
Nagy K., Tephnadze G.
Open Mathematics
|
2014
|
tom 12
|
nr 8
1214-1228
EN
The main aim of this paper is to investigate the Walsh-Marcinkiewicz means on the Hardy space H p, when 0 < p < 2/3. We define a weighted maximal operator of Walsh-Marcinkiewicz means and establish some of its properties. With its aid we provide a necessary and sufficient condition for convergence of the Walsh-Marcinkiewicz means in terms of modulus of continuity on the Hardy space H p, and prove a strong convergence theorem for the Walsh-Marcinkiewicz means.
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