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

Flavia Colonna (2013)

Open Mathematics

Let ψ and φ be analytic functions on the open unit disk $𝔻$ with φ( $𝔻$ ) ⊆ $𝔻$ . 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 $𝒟$ 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...

Numerical range of operators acting on Banach spaces

Khadijeh Jahedi, Bahmann Yousefi (2012)

Czechoslovak Mathematical Journal

The aim of the paper is to propose a definition of numerical range of an operator on reflexive Banach spaces. Under this definition the numerical range will possess the basic properties of a canonical numerical range. We will determine necessary and sufficient conditions under which the numerical range of a composition operator on a weighted Hardy space is closed. We will also give some necessary conditions to show that when the closure of the numerical range of a composition operator on a small...

On extended eigenvalues and extended eigenvectors of truncated shift

Hasan Alkanjo (2013)

Concrete Operators

In this paper we consider the truncated shift operator Su on the model space K2u := H2 θ uH2. We say that a complex number λ is an extended eigenvalue of Su if there exists a nonzero operator X, called extended eigenvector associated to λ, and satisfying the equation SuX = λXSu. We give a complete description of the set of extended eigenvectors of Su, in the case of u is a Blaschke product..

On some spaces of holomorphic functions of exponential growth on a half-plane

Marco M. Peloso, Maura Salvatori (2016)

Concrete Operators

In this paper we study spaces of holomorphic functions on the right half-plane R, that we denote by Mpω, whose growth conditions are given in terms of a translation invariant measure ω on the closed half-plane R. Such a measure has the form ω = ν ⊗ m, where m is the Lebesgue measure on R and ν is a regular Borel measure on [0, +∞). We call these spaces generalized Hardy–Bergman spaces on the half-plane R. We study in particular the case of ν purely atomic, with point masses on an arithmetic progression...

On the generalized Hardy spaces.

Fatehi, M. (2010)

Abstract and Applied Analysis

On the norm of certain weighted composition operators on the Hardy space.

Shaabani, M.Haji, Khani Robati, B. (2009)

Abstract and Applied Analysis

On weighted Hardy spaces on the unit disk

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

Banach Center Publications

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.

Outers for noncommutative $H^{p}$ revisited

David P. Blecher, Louis E. Labuschagne (2013)

Studia Mathematica

We continue our study of outer elements of the noncommutative $H^{p}$ spaces associated with Arveson’s subdiagonal algebras. We extend our generalized inner-outer factorization theorem, and our characterization of outer elements, to include the case of elements with zero determinant. In addition, we make several further contributions to the theory of outers. For example, we generalize the classical fact that outers in $H^{p}$ actually satisfy the stronger condition that there exist aₙ ∈ A with haₙ ∈ Ball(A)...

Pointwise inequalities of logarithmic type in Hardy-Hölder spaces

Slim Chaabane, Imed Feki (2014)

Czechoslovak Mathematical Journal

We prove some optimal logarithmic estimates in the Hardy space $H^{\infty} (G)$ with Hölder regularity, where $G$ is the open unit disk or an annular domain of $ℂ$ . These estimates extend the results established by S. Chaabane and I. Feki in the Hardy-Sobolev space $H^{k, \infty}$ of the unit disk and those of I. Feki in the case of an annular domain. The proofs are based on a variant of Hardy-Landau-Littlewood inequality for Hölder functions. As an application of these estimates, we study the stability of both the Cauchy problem...

Products of Toeplitz operators and Hankel operators

Yufeng Lu, Linghui Kong (2014)

Studia Mathematica

We first determine when the sum of products of Hankel and Toeplitz operators is equal to zero; then we characterize when the product of a Toeplitz operator and a Hankel operator is a compact perturbation of a Hankel operator or a Toeplitz operator and when it is a finite rank perturbation of a Toeplitz operator.

Properties of harmonic conjugates

Paweł Sobolewski (2008)

Annales UMCS, Mathematica

We give a new proof of Hardy and Littlewood theorem concerning harmonic conjugates of functions u such that ∫D |u(z)|pdA(z) < ∞, 0 < p ≤ 1. We also obtain an inequality for integral means of such harmonic functions u.

Sharp endpoint results for imaginary powers and Riesz transforms on certain noncompact manifolds

Giancarlo Mauceri, Stefano Meda, Maria Vallarino (2014)

Studia Mathematica

We consider a complete connected noncompact Riemannian manifold M with bounded geometry and spectral gap. We prove that the imaginary powers of the Laplacian and the Riesz transform are bounded from the Hardy space X¹(M), introduced in previous work of the authors, to L¹(M).

Similarity of operators and geometry of eigenvector bundles.

H. K. Kwon, S. Treil (2009)

Publicacions Matemàtiques

Some Banach spaces of Dirichlet series

Maxime Bailleul, Pascal Lefèvre (2015)

Studia Mathematica

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 between...

The canonical injection of the Hardy-Orlicz space $H^{Ψ}$ into the Bergman-Orlicz space $^{Ψ}$

Pascal Lefèvre, Daniel Li, Hervé Queffélec, Luis Rodríguez-Piazza (2011)

Studia Mathematica

We study the canonical injection from the Hardy-Orlicz space $H^{Ψ}$ into the Bergman-Orlicz space $^{Ψ}$ .

The Dynamics of Inner Functions. / Claus I. Doering; Ricardo Mané.

Ricardo Mané, Claus I. Doering (1991)

Ensaios Matemáticos

The numerical range of Toeplitz operator on the polydisk.

Gu, Dinggui (2009)

Abstract and Applied Analysis

Uniform minimality, unconditionality and interpolation in backward shift invariant subspaces

Eric Amar, Andreas Hartmann (2010)

Annales de l’institut Fourier

We discuss relations between uniform minimality, unconditionality and interpolation for families of reproducing kernels in backward shift invariant subspaces. This class of spaces contains as prominent examples the Paley-Wiener spaces for which it is known that uniform minimality does in general neither imply interpolation nor unconditionality. Hence, contrarily to the situation of standard Hardy spaces (and of other scales of spaces), changing the size of the space seems necessary to deduce unconditionality...

[unknown]

Frédéric Bayart, Hervé Queffélec, Kristian Seip (0)

Annales de l’institut Fourier

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