Jensen measures and unbounded $B-$regular domains in ${\mathbf{C}}^n$

Quang Dieu Nguyen; Dau Hoang Hung

Displaying similar documents to “Jensen measures and unbounded $B -$ regular domains in $C^{n}$ ”

A linear extension operator for Whitney fields on closed o-minimal sets

Wiesław Pawłucki (2008)

Annales de l’institut Fourier

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A continuous linear extension operator, different from Whitney’s, for $𝒞^{p}$ -Whitney fields (p finite) on a closed o-minimal subset of $ℝ^{n}$ is constructed. The construction is based on special geometrical properties of o-minimal sets earlier studied by K. Kurdyka with the author.

Strong $q$ -variation inequalities for analytic semigroups

Christian Le Merdy, Quanhua Xu (2012)

Annales de l’institut Fourier

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Let $T : L^{p} (Ω) \to L^{p} (Ω)$ be a positive contraction, with $1 < p < \infty$ . Assume that $T$ is analytic, that is, there exists a constant $K \geq 0$ such that $∥ T^{n} - T^{n - 1} ∥ \leq K / n$ for any integer $n \geq 1$ . Let $2 < q < \infty$ and let $v^{q}$ be the space of all complex sequences with a finite strong $q$ -variation. We show that for any $x \in L^{p} (Ω)$ , the sequence ${([T^{n} (x)] (λ))}_{n \geq 0}$ belongs to $v^{q}$ for almost every $λ \in Ω$ , with an estimate $∥ {(T^{n} (x))}_{n \geq 0} ∥_{L^{p} (v^{q})} \leq C {∥ x ∥}_{p}$ . If we remove the analyticity assumption, we obtain an estimate $∥ {(M_{n} (T) x)}_{n \geq 0} ∥_{L^{p} (v^{q})} \leq C {∥ x ∥}_{p}$ , where $M_{n} (T) = {(n + 1)}^{- 1} \sum_{k = 0}^{n} T^{k}$ denotes the ergodic average of $T$ . We also obtain similar results for strongly continuous semigroups...

Embedding theorems for Müntz spaces

Isabelle Chalendar, Emmanuel Fricain, Dan Timotin (2011)

Annales de l’institut Fourier

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We discuss boundedness and compactness properties of the embedding $M_{Λ}^{1} \subset L^{1} (μ)$ , where $M_{Λ}^{1}$ is the closed linear span of the monomials $x^{λ_{n}}$ in $L^{1} ([0, 1])$ and $μ$ is a finite positive Borel measure on the interval $[0, 1]$ . In particular, we introduce a class of “sublinear” measures and provide a rather complete solution of the embedding problem for the class of quasilacunary sequences $Λ$ . Finally, we show how one can recapture some of Al Alam’s results on boundedness and the essential norm of weighted composition operators...

Holomorphic retractions and boundary Berezin transforms

Jonathan Arazy, Miroslav Engliš, Wilhelm Kaup (2009)

Annales de l’institut Fourier

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In an earlier paper, the first two authors have shown that the convolution of a function $f$ continuous on the closure of a Cartan domain and a $K$ -invariant finite measure $μ$ on that domain is again continuous on the closure, and, moreover, its restriction to any boundary face $F$ depends only on the restriction of $f$ to $F$ and is equal to the convolution, in $F$ , of the latter restriction with some measure $μ_{F}$ on $F$ uniquely determined by $μ$ . In this article, we give an explicit formula for $μ_{F}$ in...

Extremal domains for the first eigenvalue of the Laplace-Beltrami operator

Frank Pacard, Pieralberto Sicbaldi (2009)

Annales de l’institut Fourier

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We prove the existence of extremal domains with small prescribed volume for the first eigenvalue of Laplace-Beltrami operator in some Riemannian manifold. These domains are close to geodesic spheres of small radius centered at a nondegenerate critical point of the scalar curvature.

Displaying similar documents to “Jensen measures and unbounded B - regular domains in C n ”

A linear extension operator for Whitney fields on closed o-minimal sets

Strong q -variation inequalities for analytic semigroups

Embedding theorems for Müntz spaces

Holomorphic retractions and boundary Berezin transforms

Extremal domains for the first eigenvalue of the Laplace-Beltrami operator

Displaying similar documents to “Jensen measures and unbounded $B -$ regular domains in $C^{n}$ ”

Strong $q$ -variation inequalities for analytic semigroups