Mean values and associated measures of $\delta $-subharmonic functions

Neil A. Watson

Displaying similar documents to “Mean values and associated measures of $δ$ -subharmonic functions”

On Ordinary and Standard Lebesgue Measures on $ℝ^{\infty}$

Gogi Pantsulaia (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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New concepts of Lebesgue measure on $ℝ^{\infty}$ are proposed and some of their realizations in the ZFC theory are given. Also, it is shown that Baker’s both measures [1], [2], Mankiewicz and Preiss-Tišer generators [6] and the measure of [4] are not α-standard Lebesgue measures on $ℝ^{\infty}$ for α = (1,1,...).

Some properties of the balayage of measures on a harmonic space

Corneliu Constantinescu (1967)

Annales de l'institut Fourier

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On démontre plusieurs théorèmes concernant le balayage des mesures sur un espace harmonique satisfaisant aux axiomes de Bauer, parmi lesquels nous indiquons les suivants : a) la balayée $μ_{A \cup B}$ d’une mesure $μ$ sur la réunion $μ^{A} \lor μ^{B}$ (dans l’espace de Riesz de mesure) ; b) $ϵ_{x}^{A} \neq ϵ_{x}$ caractérise l’effilement de $A$ en $x$ ; c) il existe un potentiel fini et continue $p$ tel que pour tout ensemble $A {x | {\hat{R}}_{p} (x) < p (x)}$ est exactement l’ensemble des points où $A$ est effilé ; d) $μ^{A}$ est portée par la fermeture fine de $A$ ; e) si $A$ et $B$ sont...

The max norm in $R^{n}$ -isometries and measure

Regina Cohen, James W. Fickett (1982)

Colloquium Mathematicae

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Invariance of the Gibbs measure for the Benjamin–Ono equation

Yu Deng (2015)

Journal of the European Mathematical Society

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In this paper we consider the periodic Benjemin-Ono equation.We establish the invariance of the Gibbs measure associated to this equation, thus answering a question raised in Tzvetkov [28]. As an intermediate step, we also obtain a local well-posedness result in Besov-type spaces rougher than $L^{2}$ , extending the $L^{2}$ well-posedness result of Molinet [20].

Triebel-Lizorkin spaces with non-doubling measures

Yongsheng Han, Dachun Yang (2004)

Studia Mathematica

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Suppose that μ is a Radon measure on $ℝ^{d}$ , which may be non-doubling. The only condition assumed on μ is a growth condition, namely, there is a constant C₀ > 0 such that for all x ∈ supp(μ) and r > 0, μ(B(x,r)) ≤ C₀rⁿ, where 0 < n ≤ d. The authors provide a theory of Triebel-Lizorkin spaces $Ḟ_{p q}^{s} (μ)$ for 1 < p < ∞, 1 ≤ q ≤ ∞ and |s| < θ, where θ > 0 is a real number which depends on the non-doubling measure μ, C₀, n and d. The method does not use the vector-valued maximal function...

Unique Bernoulli $g$ -measures

Anders Johansson, Anders Öberg, Mark Pollicott (2012)

Journal of the European Mathematical Society

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We improve and subsume the conditions of Johansson and Öberg and Berbee for uniqueness of a $g$ -measure, i.e., a stationary distribution for chains with complete connections. In addition, we prove that these unique $g$ -measures have Bernoulli natural extensions. We also conclude that we have convergence in the Wasserstein metric of the iterates of the adjoint transfer operator to the $g$ -measure.

Quantization Dimension Estimate of Inhomogeneous Self-Similar Measures

Mrinal Kanti Roychowdhury (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

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We consider an inhomogeneous measure μ with the inhomogeneous part a self-similar measure ν, and show that for a given r ∈ (0,∞) the lower and the upper quantization dimensions of order r of μ are bounded below by the quantization dimension $D_{r} (ν)$ of ν and bounded above by a unique number $κ_{r} \in (0, \infty)$ , related to the temperature function of the thermodynamic formalism that arises in the multifractal analysis of μ.

When is a Riesz distribution a complex measure?

Alan D. Sokal (2011)

Bulletin de la Société Mathématique de France

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Let $ℛ_{α}$ be the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by $α \in ℂ$ . I give an elementary proof of the necessary and sufficient condition for $ℛ_{α}$ to be a locally finite complex measure (= complex Radon measure).

Interpolating sequences, Carleson measures and Wirtinger inequality

Eric Amar (2008)

Annales Polonici Mathematici

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Let S be a sequence of points in the unit ball of ℂⁿ which is separated for the hyperbolic distance and contained in the zero set of a Nevanlinna function. We prove that the associated measure $μ_{S} : = \sum_{a \in S} (1 - | a | ²) ⁿ δ_{a}$ is bounded, by use of the Wirtinger inequality. Conversely, if X is an analytic subset of such that any δ -separated sequence S has its associated measure $μ_{S}$ bounded by C/δⁿ, then X is the zero set of a function in the Nevanlinna class of . As an easy consequence, we prove that if S is a dual...

Estimates of capacity of self-similar measures

Jozef Myjak, Tomasz Szarek (2002)

Annales Polonici Mathematici

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We give lower and upper estimates of the capacity of self-similar measures generated by iterated function systems $(S_{i}, p_{i}) : i = 1, . . ., N$ where $S_{i}$ are bi-lipschitzean transformations.

Essential norms of the Neumann operator of the arithmetical mean

Josef Král, Dagmar Medková (2001)

Mathematica Bohemica

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Let $K \subset ℝ^{m}$ ( $m \geq 2$ ) be a compact set; assume that each ball centered on the boundary $B$ of $K$ meets $K$ in a set of positive Lebesgue measure. Let $C_{0}^{(1)}$ be the class of all continuously differentiable real-valued functions with compact support in $ℝ^{m}$ and denote by $σ_{m}$ the area of the unit sphere in $ℝ^{m}$ . With each $ϕ \in C_{0}^{(1)}$ we associate the function $W_{K} ϕ (z) = \frac{1}{σ_{m}} \underset{ℝ^{m} ∖ K}{\to} \int g r a d ϕ (x) \cdot \frac{z - x}{{| z - x |}^{m}} x$ of the variable $z \in K$ (which is continuous in $K$ and harmonic in $K ∖ B$ ). $W_{K} ϕ$ depends only on the restriction ${ϕ |}_{B}$ of $ϕ$ to the boundary $B$ of $K$ . This gives rise to a linear operator $W_{K}$ ...

Sets of $β$ -expansions and the Hausdorff measure of slices through fractals

Tom Kempton (2016)

Journal of the European Mathematical Society

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We study natural measures on sets of $β$ -expansions and on slices through self similar sets. In the setting of $β$ -expansions, these allow us to better understand the measure of maximal entropy for the random $β$ -transformation and to reinterpret a result of Lindenstrauss, Peres and Schlag in terms of equidistribution. Each of these applications is relevant to the study of Bernoulli convolutions. In the fractal setting this allows us to understand how to disintegrate Hausdorff measure by slicing,...

Algebraic genericity of strict-order integrability

Luis Bernal-González (2010)

Studia Mathematica

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We provide sharp conditions on a measure μ defined on a measurable space X guaranteeing that the family of functions in the Lebesgue space $L^{p} (μ, X)$ (p ≥ 1) which are not q-integrable for any q > p (or any q < p) contains large subspaces of $L^{p} (μ, X)$ (without zero). This improves recent results due to Aron, García, Muñoz, Palmberg, Pérez, Puglisi and Seoane. It is also shown that many non-q-integrable functions can even be obtained on any nonempty open subset of X, assuming that X is a topological...

H¹ and BMO for certain locally doubling metric measure spaces of finite measure

Andrea Carbonaro, Giancarlo Mauceri, Stefano Meda (2010)

Colloquium Mathematicae

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In a previous paper the authors developed an H¹-BMO theory for unbounded metric measure spaces (M,ρ,μ) of infinite measure that are locally doubling and satisfy two geometric properties, called “approximate midpoint” property and “isoperimetric” property. In this paper we develop a similar theory for spaces of finite measure. We prove that all the results that hold in the infinite measure case have their counterparts in the finite measure case. Finally, we show that the theory applies...

A remark on a lower envelope principle

Masanori Kishi (1964)

Annales de l'institut Fourier

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Soit $Ω$ un espace topologique localement séparé et soit $G$ un noyau (symétrique ou non) positif et continu au sens large dans $Ω$ . Si $G$ satisfait au principe de domination ordinaire et si le noyau adjoint $\overset{ˇ}{G}$ est régulier, alors $X$ satisfait au principe de l’enveloppe inférieure sur tout compact, c’est-à-dire, pour tout compact $K \subset Ω$ et toutes mesures positives $μ$ et $ν$ (l’une d’elles d’énergie finie), il existe une mesure positive $λ$ portée par $K$ telle que $G λ = G μ \land G ν$ à p.p.p. sur $K$ . Ici nous considérons le...

Displaying similar documents to “Mean values and associated measures of δ -subharmonic functions”

Displaying similar documents to “Mean values and associated measures of $δ$ -subharmonic functions”