Disc formulas for the weighted Siciak-Zahariuta extremal function

Benedikt Steinar Magnússon; Ragnar Sigurdsson

Displaying similar documents to “Disc formulas for the weighted Siciak-Zahariuta extremal function”

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 $L^{\infty}$ .

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.

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.

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

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.

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.

Existence of solutions to the (rot,div)-system in L₂-weighted spaces

Wojciech M. Zajączkowski (2009)

Applicationes Mathematicae

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The existence of solutions to the elliptic problem rot v = w, div v = 0 in Ω ⊂ ℝ³, ${v \cdot n ̅ |}_{S} = 0$ , S = ∂Ω, in weighted Hilbert spaces is proved. It is assumed that Ω contains an axis L and the weight is a negative power of the distance to the axis. The main part of the proof is devoted to examining solutions in a neighbourhood of L. Their existence in Ω follows by regularization.

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.

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...

Monotonicity of generalized weighted mean values

Alfred Witkowski (2004)

Colloquium Mathematicae

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The author gives a new simple proof of monotonicity of the generalized extended mean values $M (r, s) = \leq {((\int f^{s} d μ) / (\int f^{r} d μ))}^{1 / (s - r)}$ introduced by F. Qi.

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

Earl Berkson, T. A. Gillespie (1990)

Colloquium Mathematicae

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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...

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...

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.

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.

On mean value properties involving a logarithm-type weight

Nikolai G. Kuznecov (2024)

Mathematica Bohemica

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Two new assertions characterizing analytically disks in the Euclidean plane $ℝ^{2}$ are proved. Weighted mean value property of positive solutions to the Helmholtz and modified Helmholtz equations are used for this purpose; the weight has a logarithmic singularity. The obtained results are compared with those without weight that were found earlier.

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.

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.

Weighted bounds for variational Fourier series

Yen Do, Michael Lacey (2012)

Studia Mathematica

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For 1 < p < ∞ and for weight w in $A_{p}$ , we show that the r-variation of the Fourier sums of any function f in $L^{p} (w)$ is finite a.e. for r larger than a finite constant depending on w and p. The fact that the variation exponent depends on w is necessary. This strengthens previous work of Hunt-Young and is a weighted extension of a variational Carleson theorem of Oberlin-Seeger-Tao-Thiele-Wright. The proof uses weighted adaptation of phase plane analysis and a weighted extension of a variational...

Existence of solutions to the Poisson equation in $L_{p}$ -weighted spaces

Joanna Rencławowicz, Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

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We examine the Poisson equation with boundary conditions on a cylinder in a weighted space of $L_{p}$ , p≥ 3, type. The weight is a positive power of the distance from a distinguished plane. To prove the existence of solutions we use our result on existence in a weighted L₂ space.

Weighted $L^{\infty}$ -estimates for Bergman projections

José Bonet, Miroslav Engliš, Jari Taskinen (2005)

Studia Mathematica

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We consider Bergman projections and some new generalizations of them on weighted $L^{\infty} ()$ -spaces. A new reproducing formula is obtained. We show the boundedness of these projections for a large family of weights v which tend to 0 at the boundary with a polynomial speed. These weights may even be nonradial. For logarithmically decreasing weights bounded projections do not exist. In this case we instead consider the projective description problem for holomorphic inductive limits.

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...

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. ...

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.