A generalization of the Aleksandrov operator and adjoints of weighted composition operators

Eva A. Gallardo-Gutiérrez; Jonathan R. Partington

Displaying similar documents to “A generalization of the Aleksandrov operator and adjoints of weighted composition operators”

Centered weighted composition operators via measure theory

Mohammad Reza Jabbarzadeh, Mehri Jafari Bakhshkandi (2018)

Mathematica Bohemica

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We describe the centered weighted composition operators on $L^{2} (Σ)$ in terms of their defining symbols. Our characterizations extend Embry-Wardrop-Lambert’s theorem on centered composition operators.

Complex symmetric weighted composition operators on the Hardy space

Cao Jiang, Shi-An Han, Ze-Hua Zhou (2020)

Czechoslovak Mathematical Journal

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This paper identifies a class of complex symmetric weighted composition operators on $H^{2} (𝔻)$ that includes both the unitary and the Hermitian weighted composition operators, as well as a class of normal weighted composition operators identified by Bourdon and Narayan. A characterization of algebraic weighted composition operators with degree no more than two is provided to illustrate that the weight function of a complex symmetric weighted composition operator is not necessarily linear fractional. ...

On weighted composition operators acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces

Elke Wolf (2011)

Annales Polonici Mathematici

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Let ϕ: → and ψ: → ℂ be analytic maps. They induce a weighted composition operator $ψ C_{ϕ}$ acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces. Under some assumptions on the weights we give a characterization for such an operator to be bounded in terms of the weights involved as well as the functions ψ and ϕ

Weighted composition operators between weighted Banach spaces of holomorphic functions and weighted Bloch type space

Elke Wolf (2009)

Annales Polonici Mathematici

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Let ϕ: → and ψ: → ℂ be analytic maps. They induce a weighted composition operator $ψ C_{ϕ}$ acting between weighted Banach spaces of holomorphic functions and weighted Bloch type spaces. Under some assumptions on the weights we give a necessary as well as a sufficient condition for such an operator to be bounded resp. compact.

The John-Nirenberg type inequality for non-doubling measures

Yoshihiro Sawano, Hitoshi Tanaka (2007)

Studia Mathematica

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X. Tolsa defined a space of BMO type for positive Radon measures satisfying some growth condition on $ℝ^{d}$ . This new BMO space is very suitable for the Calderón-Zygmund theory with non-doubling measures. Especially, the John-Nirenberg type inequality can be recovered. In the present paper we introduce a localized and weighted version of this inequality and, as applications, we obtain some vector-valued inequalities and weighted inequalities for Morrey spaces.

Commutant of multiplication operators in weighted Bergman spaces on polydisk

Ali Abkar (2020)

Czechoslovak Mathematical Journal

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We study a certain operator of multiplication by monomials in the weighted Bergman space both in the unit disk of the complex plane and in the polydisk of the $n$ -dimensional complex plane. Characterization of the commutant of such operators is given.

Characterization of associate spaces of weighted Lorentz spaces with applications

Amiran Gogatishvili, Luboš Pick, Filip Soudský (2014)

Studia Mathematica

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We characterize associate spaces of weighted Lorentz spaces GΓ(p,m,w) and present some applications of this result including necessary and sufficient conditions for a Sobolev-type embedding into $L^{\infty}$ .

Embeddings of doubling weighted Besov spaces

Dorothee D. Haroske, Philipp Skandera (2014)

Banach Center Publications

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We study continuous embeddings of Besov spaces of type $B_{p, q}^{s} (ℝ ⁿ, w)$ , where s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞, and the weight w is doubling. This approach generalises recent results about embeddings of Muckenhoupt weighted Besov spaces. Our main argument relies on appropriate atomic decomposition techniques of such weighted spaces; here we benefit from earlier results by Bownik. In addition, we discuss some other related weight classes briefly and compare corresponding results.

Weighted composition operators on weighted Lorentz spaces

İlker Eryilmaz (2012)

Colloquium Mathematicae

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The boundedness, compactness and closedness of the range of weighted composition operators acting on weighted Lorentz spaces L(p,q,wdμ) for 1 < p ≤ ∞, 1 ≤ q ≤ ∞ are characterized.

Multilinear Calderón-Zygmund operators on weighted Hardy spaces

Wenjuan Li, Qingying Xue, Kôzô Yabuta (2010)

Studia Mathematica

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Grafakos-Kalton [Collect. Math. 52 (2001)] discussed the boundedness of multilinear Calderón-Zygmund operators on the product of Hardy spaces. Then Lerner et al. [Adv. Math. 220 (2009)] defined $A_{p ⃗}$ weights and built a theory of weights adapted to multilinear Calderón-Zygmund operators. In this paper, we combine the above results and obtain some estimates for multilinear Calderón-Zygmund operators on weighted Hardy spaces and also obtain a weighted multilinear version of an inequality for...

The spectral decomposition of weighted shifts and the $A^{p}$ condition

Earl Berkson, T. A. Gillespie (1990)

Colloquium Mathematicae

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Two-weighted criteria for integral transforms with multiple kernels

Vakhtang Kokilashvili, Alexander Meskhi (2006)

Banach Center Publications

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Necessary and sufficient conditions governing two-weight $L^{p}$ norm estimates for multiple Hardy and potential operators are presented. Two-weight inequalities for potentials defined on nonhomogeneous spaces are also discussed. Sketches of the proofs for most of the results are given.

ω-Calderón-Zygmund operators

Sijue Wu (1995)

Studia Mathematica

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We prove a T1 theorem and develop a version of Calderón-Zygmund theory for ω-CZO when $ω \in A_{\infty}$ .

Some Applications of new Modified q-Szász–Mirakyan Operators

Ramesh P. PATHAK, Shiv Kumar SAHOO (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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This paper we introducing a new sequence of positive q-integral new Modified q-Szász-Mirakyan Operators. We show that it is a weighted approximation process in the polynomial space of continuous functions defined on $[0, \infty)$ . Weighted statistical approximation theorem, Korovkin-type theorems for fuzzy continuous functions, an estimate for the rate of convergence and some properties are also obtained for these operators.

Boundedness of Riesz transforms on weighted Carleson measure spaces

Ming-Yi Lee (2012)

Studia Mathematica

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Let w be in the Muckenhoupt $A_{\infty}$ weight class. We show that the Riesz transforms are bounded on the weighted Carleson measure space $C M O_{w}^{p}$ , the dual of the weighted Hardy space $H_{w}^{p}$ , 0 < p ≤ 1.

On the Banach-Stone problem

Jyh-Shyang Jeang, Ngai-Ching Wong (2003)

Studia Mathematica

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Let X and Y be locally compact Hausdorff spaces, let E and F be Banach spaces, and let T be a linear isometry from C₀(X,E) into C₀(Y,F). We provide three new answers to the Banach-Stone problem: (1) T can always be written as a generalized weighted composition operator if and only if F is strictly convex; (2) if T is onto then T can be written as a weighted composition operator in a weak sense; and (3) if T is onto and F does not contain a copy of $ℓ ₂^{\infty}$ then T can be written as a weighted...

Disjoint hypercyclic powers of weighted translations on groups

Liang Zhang, Hui-Qiang Lu, Xiao-Mei Fu, Ze-Hua Zhou (2017)

Czechoslovak Mathematical Journal

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Let $G$ be a locally compact group and let $1 \leq p < \infty .$ Recently, Chen et al. characterized hypercyclic, supercyclic and chaotic weighted translations on locally compact groups and their homogeneous spaces. There has been an increasing interest in studying the disjoint hypercyclicity acting on various spaces of holomorphic functions. In this note, we will study disjoint hypercyclic and disjoint supercyclic powers of weighted translation operators on the Lebesgue space $L^{p} (G)$ in terms of the weights. Sufficient...

Statistical approximation by positive linear operators

O. Duman, C. Orhan (2004)

Studia Mathematica

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Using A-statistical convergence, we prove a Korovkin type approximation theorem which concerns the problem of approximating a function f by means of a sequence Tₙ(f;x) of positive linear operators acting from a weighted space $C_{ϱ ₁}$ into a weighted space $B_{ϱ ₂}$ .

Singularities in Muckenhoupt weighted function spaces

Dorothee D. Haroske (2008)

Banach Center Publications

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We study weighted function spaces of Lebesgue, Besov and Triebel-Lizorkin type where the weight function belongs to some Muckenhoupt $_{p}$ class. The singularities of functions in these spaces are characterised by means of envelope functions.

Non-compact Littlewood-Paley theory for non-doubling measures

Michael Wilson (2007)

Studia Mathematica

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We prove weighted Littlewood-Paley inequalities for linear sums of functions satisfying mild decay, smoothness, and cancelation conditions. We prove these for general “regular” measure spaces, in which the underlying measure is not assumed to satisfy any doubling condition. Our result generalizes an earlier result of the author, proved on $ℝ^{d}$ with Lebesgue measure. Our proof makes essential use of the technique of random dyadic grids, due to Nazarov, Treil, and Volberg.

The Properties of the Weighted Space $H_{2, α}^{k} (Ω)$ and Weighted Set $W_{2, α}^{k} (Ω, δ)$

V.A. Rukavishnikov, E.V. Matveeva, E.I. Rukavishnikova (2018)

Communications in Mathematics

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We study the properties of the weighted space $H_{2, α}^{k} (Ω)$ and weighted set $W_{2, α}^{k} (Ω, δ)$ for boundary value problem with singularity.

Composition operators between generally weighted Bloch spaces and $Q_{log}^{q}$ space.

Li, Haiying, Liu, Peide (2008)

Banach Journal of Mathematical Analysis [electronic only]

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Weighted composition operators between a weighted-type space and the Hardy space on the unit ball

Ze-Hua Zhou, Yu-Xia Liang, Xing-Tang Dong (2012)

Annales Polonici Mathematici

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This paper characterizes the boundedness and compactness of weighted composition operators between a weighted-type space and the Hardy space on the unit ball of ℂⁿ.

$^{\infty}$ -vectors and boundedness

Jan Stochel, F. H. Szafraniec (1997)

Annales Polonici Mathematici

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The following two questions as well as their relationship are studied: (i) Is a closed linear operator in a Banach space bounded if its $^{\infty}$ -vectors coincide with analytic (or semianalytic) ones? (ii) When are the domains of two successive powers of the operator in question equal? The affirmative answer to the first question is established in case of paranormal operators. All these investigations are illustrated in the context of weighted shifts.

Existence of solutions to the nonstationary Stokes system in $H_{- μ}^{2, 1}$ , μ ∈ (0,1), in a domain with a distinguished axis. Part 1. Existence near the axis in 2d

W. M. Zajączkowski (2007)

Applicationes Mathematicae

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We consider the nonstationary Stokes system with slip boundary conditions in a bounded domain which contains some distinguished axis. We assume that the data functions belong to weighted Sobolev spaces with the weight equal to some power function of the distance to the axis. The aim is to prove the existence of solutions in corresponding weighted Sobolev spaces. The proof is divided into three parts. In the first, the existence in 2d in weighted spaces near the axis is shown. In the...