منابع مشابه
Carleson Measures and Balayage for Bergman Spaces of Strongly Pseudoconvex Domains
Given a bounded strongly pseudoconvex domain D in C with smooth boundary, we characterize (p, q, α)-Bergman Carleson measures for 0 < p < ∞, 0 < q < ∞, and α > −1. As an application, we show that the Bergman space version of the balayage of a Bergman Carleson measure on D belongs to BMO in the Kobayashi metric.
متن کاملUniform Rectifiability, Carleson Measure Estimates, and Approximation of Harmonic Functions
Let E ⊂ Rn+1, n ≥ 2, be a uniformly rectifiable set of dimension n. Then bounded harmonic functions in Ω := Rn+1 \ E satisfy Carleson measure estimates, and are “ε-approximable”. Our results may be viewed as generalized versions of the classical F. and M. Riesz theorem, since the estimates that we prove are equivalent, in more topologically friendly settings, to quantitative mutual absolute con...
متن کاملCarleson Measure in Bergman-Orlicz Space of Polydisc
and Applied Analysis 3 2. Main Results and Proofs Lemma 2.1. For α α1, . . . , αn ∈ D, let uα z1, . . . , zn ∏n j 1 1 − |αj |2 / 1 − αjzj . Then uα z1, . . . , zn ∈ Lφa D , and ‖uα z ‖σn ≤ 1 φ−1 ∏n j 1 ( 1/δ2 j )) . 2.1 Proof. It is easy to see that ‖uα z ‖∞ ∏n j 1 1 |αj | / 1 − |αj | 2 ∏n j 1 2 − δj /δj . Since φ 0 0, the convexity of φ implies φ ax ≤ aφ x for 0 ≤ a ≤ 1. Hence, for every C > 0...
متن کاملOn the Carleson measure criterion in linear systems theory
In Ho and Russell (SIAM J Control Optim 21(4):614–640, 1983), and Weiss (Syst Control Lett 10(1): 79–82, 1988), a Carleson measure criterion for admissibility of one-dimensional input elements with respect to diagonal semigroups is given.We extend their results from the Hilbert space situation (L2-admissibility on the state space 2) to the more general situation of L p-admissibility on the stat...
متن کاملCarleson and Vanishing Carleson Measures on Radial Trees
We extend a discrete version of an extension of Carleson’s theorem proved in [5] to a large class of trees T that have certain radial properties. We introduce the geometric notion of s-vanishing Carleson measure on such a tree T (with s ≥ 1) and give several characterizations of such measures. Given a measure σ on T and p ≥ 1, let Lp(σ) denote the space of functions g defined on T such that |g|...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2009
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnp222