Weighted $L^{∞}$-estimates for Bergman projections

José Bonet; Miroslav Engliš; Jari Taskinen

Displaying similar documents to “Weighted $L^{\infty}$ -estimates for Bergman projections”

Weighted composition operators from Zygmund spaces to Bloch spaces on the unit ball

Yu-Xia Liang, Chang-Jin Wang, Ze-Hua Zhou (2015)

Annales Polonici Mathematici

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Let H() denote the space of all holomorphic functions on the unit ball ⊂ ℂⁿ. Let φ be a holomorphic self-map of and u∈ H(). The weighted composition operator $u C_{φ}$ on H() is defined by $u C_{φ} f (z) = u (z) f (φ (z))$ . We investigate the boundedness and compactness of $u C_{φ}$ induced by u and φ acting from Zygmund spaces to Bloch (or little Bloch) spaces in the unit ball.

The Bergman projection on weighted spaces: L¹ and Herz spaces

Oscar Blasco, Salvador Pérez-Esteva (2002)

Studia Mathematica

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We find necessary and sufficient conditions on radial weights w on the unit disc so that the Bergman type projections of Forelli-Rudin are bounded on L¹(w) and in the Herz spaces $K_{p}^{q} (w)$ .

Weighted sub-Bergman Hilbert spaces

Maria Nowak, Renata Rososzczuk (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We consider Hilbert spaces which are counterparts of the de Branges-Rovnyak spaces in the context of the weighted Bergman spaces $A_{α}^{2}$ , $- 1 < α < \infty$ . These spaces have already been studied in [8], [7], [5] and [1]. We extend some results from these papers.

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.

The Bergman projection in spaces of entire functions

Jocelyn Gonessa, El Hassan Youssfi (2012)

Annales Polonici Mathematici

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We establish $L^{p}$ -estimates for the weighted Bergman projection on a nonsingular cone. We apply these results to the weighted Fock space with respect to the minimal norm in ℂⁿ.

Inclusion relations between harmonic Bergman-Besov and weighted Bloch spaces on the unit ball

Ömer Faruk Doğan, Adem Ersin Üreyen (2019)

Czechoslovak Mathematical Journal

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We consider harmonic Bergman-Besov spaces $b_{α}^{p}$ and weighted Bloch spaces $b_{α}^{\infty}$ on the unit ball of $ℝ^{n}$ for the full ranges of parameters $0 < p < \infty$ , $α \in ℝ$ , and determine the precise inclusion relations among them. To verify these relations we use Carleson measures and suitable radial differential operators. For harmonic Bergman spaces various characterizations of Carleson measures are known. For weighted Bloch spaces we provide a characterization when $α > 0$ .

Compactness of composition operators acting on weighted Bergman-Orlicz spaces

Ajay K. Sharma, S. Ueki (2012)

Annales Polonici Mathematici

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We characterize compact composition operators acting on weighted Bergman-Orlicz spaces $_{α}^{ψ} = f \in H () : \int_{} ψ (| f (z) |) d A_{α} (z) < \infty$ , where α > -1 and ψ is a strictly increasing, subadditive convex function defined on [0,∞) and satisfying ψ(0) = 0, the growth condition $l i m_{t \to \infty} ψ (t) / t = \infty$ and the Δ₂-condition. In fact, we prove that $C_{φ}$ is compact on $_{α}^{ψ}$ if and only if it is compact on the weighted Bergman space $²_{α}$ .

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...

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.

The representation of multi-hypergraphs by set intersections

Stanisław Bylka, Jan Komar (2007)

Discussiones Mathematicae Graph Theory

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This paper deals with weighted set systems (V,,q), where V is a set of indices, $\subset 2^{V}$ and the weight q is a nonnegative integer function on . The basic idea of the paper is to apply weighted set systems to formulate restrictions on intersections. It is of interest to know whether a weighted set system can be represented by set intersections. An intersection representation of (V,,q) is defined to be an indexed family $R = {(R_{v})}_{v \in V}$ of subsets of a set S such that $| ⋂_{v \in E} R_{v} | = q (E)$ for each E ∈ . A necessary condition...

On locally convex extension of $H^{\infty}$ in the unit ball and continuity of the Bergman projection

M. Jasiczak (2003)

Studia Mathematica

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We define locally convex spaces LW and HW consisting of measurable and holomorphic functions in the unit ball, respectively, with the topology given by a family of weighted-sup seminorms. We prove that the Bergman projection is a continuous map from LW onto HW. These are the smallest spaces having this property. We investigate the topological and algebraic properties of HW.

On an integral-type operator from Privalov spaces to Bloch-type spaces

Xiangling Zhu (2011)

Annales Polonici Mathematici

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Let H(B) denote the space of all holomorphic functions on the unit ball B of ℂⁿ. Let φ be a holomorphic self-map of B and g ∈ H(B) such that g(0) = 0. We study the integral-type operator $C_{φ}^{g} f (z) = \int_{0}^{1} ℜ f (φ (t z)) g (t z) d t / t$ , f ∈ H(B). The boundedness and compactness of $C_{φ}^{g}$ from Privalov spaces to Bloch-type spaces and little Bloch-type spaces are studied

Existence of solutions to the (rot,div)-system in $L_{p}$ -weighted spaces

Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

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The existence of solutions to the elliptic problem rot v = w, div v = 0 in a bounded domain Ω ⊂ ℝ³, ${v \cdot n ̅ |}_{S} = 0$ , S = ∂Ω in weighted $L_{p}$ -Sobolev spaces is proved. It is assumed that an axis L crosses Ω and the weight is a negative power function of the distance to the axis. The main part of the proof is devoted to examining solutions of the problem in a neighbourhood of L. The existence in Ω follows from the technique of regularization.

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

Earl Berkson, T. A. Gillespie (1990)

Colloquium Mathematicae

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Natural boundary value problems for weighted form laplacians

Wojciech Kozłowski, Antoni Pierzchalski (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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The four natural boundary problems for the weighted form Laplacians $L = a d δ + b δ d, a, b > 0$ acting on polynomial differential forms in the $n$ -dimensional Euclidean ball are solved explicitly. Moreover, an algebraic algorithm for generating a solution from the boundary data is given in each case.

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 boundary behaviour of the Bergman projection on pseudoconvex domains

M. Jasiczak (2005)

Studia Mathematica

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It is shown that on strongly pseudoconvex domains the Bergman projection maps a space $L v_{k}$ of functions growing near the boundary like some power of the Bergman distance from a fixed point into a space of functions which can be estimated by the consecutive power of the Bergman distance. This property has a local character. Let Ω be a bounded, pseudoconvex set with C³ boundary. We show that if the Bergman projection is continuous on a space $E \supset L^{\infty} (Ω)$ defined by weighted-sup seminorms and equipped...

Toeplitz operators on Bergman spaces and Hardy multipliers

Wolfgang Lusky, Jari Taskinen (2011)

Studia Mathematica

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We study Toeplitz operators $T_{a}$ with radial symbols in weighted Bergman spaces $A_{μ}^{p}$ , 1 < p < ∞, on the disc. Using a decomposition of $A_{μ}^{p}$ into finite-dimensional subspaces the operator $T_{a}$ can be considered as a coefficient multiplier. This leads to new results on boundedness of $T_{a}$ and also shows a connection with Hardy space multipliers. Using another method we also prove a necessary and sufficient condition for the boundedness of $T_{a}$ for a satisfying an assumption on the positivity of certain...

On the isomorphism classes of weighted spaces of harmonic and holomorphic functions

Wolfgang Lusky (2006)

Studia Mathematica

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Let Ω be either the complex plane or the open unit disc. We completely determine the isomorphism classes of $H v = f : Ω \to ℂ h o l o m o r p h i c : s u p_{z \in Ω} | f (z) | v (z) < \infty$ and investigate some isomorphism classes of $h v = f : Ω \to ℂ h a r m o n i c : s u p_{z \in Ω} | f (z) | v (z) < \infty$ where v is a given radial weight function. Our main results show that, without any further condition on v, there are only two possibilities for Hv, namely either $H v \sim l_{\infty}$ or $H v \sim H_{\infty}$ , and at least two possibilities for hv, again $h v \sim l_{\infty}$ and $h v \sim H_{\infty}$ . We also discuss many new examples of weights.

On the geometry of the space of m-pairs of holomorphic subspaces of the n-dimensional projective space $P_{n}$ ove r an albebra $𝒜$

Е.М. Кузнецова (1986)

Trudy Geometriceskogo Seminara

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Solutions to the equation div u = f in weighted Sobolev spaces

Katrin Schumacher (2008)

Banach Center Publications

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We consider the problem div u = f in a bounded Lipschitz domain Ω, where f with $\int_{Ω} f = 0$ is given. It is shown that the solution u, constructed as in Bogovski’s approach in [1], fulfills estimates in the weighted Sobolev spaces $W_{w}^{k, q} (Ω)$ , where the weight function w is in the class of Muckenhoupt weights $A_{q}$ .

Cyclic phenomena for composition operators on weighted Bergman spaces

Anna Gori (2006)

Bollettino dell'Unione Matematica Italiana

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In the present paper we give a generalization to the family of Bergman Spaces with weight $G$ , $A^{2}_{G}$ of several results, obtained in [4] for the Hardy space $H^{2}$ , concerning the cyclic and hypercyclic behaviour of composition operators CW induced by a holomorphic self map $\varphi$ of the open unit disc $\Delta\subset\mathbb{C}$ .

Compact operators on the weighted Bergman space A¹(ψ)

Tao Yu (2006)

Studia Mathematica

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We show that a bounded linear operator S on the weighted Bergman space A¹(ψ) is compact and the predual space A₀(φ) of A¹(ψ) is invariant under S* if and only if $S k_{z} \to 0$ as z → ∂D, where $k_{z}$ is the normalized reproducing kernel of A¹(ψ). As an application, we give conditions for an operator in the Toeplitz algebra to be compact.

Lipschitz continuity in Muckenhoupt 𝓐₁ weighted function spaces

Dorothee D. Haroske (2011)

Banach Center Publications

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We study continuity envelopes of function spaces $B_{p, q}^{s} (ℝ ⁿ, w)$ and $F_{p, q}^{s} (ℝ ⁿ, w)$ where the weight belongs to the Muckenhoupt class ₁. This essentially extends partial forerunners in [13, 14]. We also indicate some applications of these results.

Polyanalytic Besov spaces and approximation by dilatations

Ali Abkar (2024)

Czechoslovak Mathematical Journal

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Using partial derivatives $\partial f / \partial z$ and $\partial f / \partial \bar{z}$ , we introduce Besov spaces of polyanalytic functions in the open unit disk, as well as in the upper half-plane. We then prove that the dilatations of functions in certain weighted polyanalytic Besov spaces converge to the same functions in norm. When restricted to the open unit disk, we prove that each polyanalytic function of degree $q$ can be approximated in norm by polyanalytic polynomials of degree at most $q$ .

On spaces of holomorphic functions in ℂⁿ

Diana D. Jiménez S., Lino F. Reséndis O., Luis M. Tovar S. (2014)

Banach Center Publications

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Following the line of Ouyang et al. (1998) to study the $_{p}$ spaces of holomorphic functions in the unit ball of ℂⁿ, we present in this paper several results and relations among $_{p} (ₙ)$ , the α-Bloch, the Dirichlet $_{p}$ and the little $_{p, 0}$ spaces.

Weighted boundedness of Toeplitz type operators related to singular integral operators with non-smooth kernel

Xiaosha Zhou, Lanzhe Liu (2013)

Colloquium Mathematicae

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Some weighted sharp maximal function inequalities for the Toeplitz type operator $T_{b} = \sum_{k = 1}^{m} T^{k, 1} M_{b} T^{k, 2}$ are established, where $T^{k, 1}$ are a fixed singular integral operator with non-smooth kernel or ±I (the identity operator), $T^{k, 2}$ are linear operators defined on the space of locally integrable functions, k = 1,..., m, and $M_{b} (f) = b f$ . The weighted boundedness of $T_{b}$ on Morrey spaces is obtained by using sharp maximal function inequalities.

Existence and regularity of solutions of some elliptic system in domains with edges

Wojciech M. Zajączkowski

Similarity:

CONTENTS1. Introduction.......................................................................52. Notation and auxiliary results............................................93. Statement of the problem (1.1)-(1.3)..............................204. The problem (3.14).........................................................225. Auxiliary results in $D_{ϑ}$ ...............................................346. Existence of solutions of (3.14) in $H_{μ}^{k} (D_{ϑ})$ ............417. Green function................................................................528....

Displaying similar documents to “Weighted L ∞ -estimates for Bergman projections”

Displaying similar documents to “Weighted $L^{\infty}$ -estimates for Bergman projections”