Abstract. We formulate and prove a Jakobson-Benedicks-Carleson type theorem on the occurence of nonuniform hyperbolicity (stochastic dynamics) in families of one-dimensional maps, based on computable starting conditions and providing explicit, computable, lower bounds for the measure of the set of selected parameters. As a first application of our results we show that the set of parameters corr...

is a Carleson measure in a Lipschitz domain Ω ⊂ R, n ≥ 1, (here δ (X) = dist (X,∂Ω)). If the harmonic measure dωL0 ∈ A∞, then dωL1 ∈ A∞. This is an analog to Theorem 2.17 in [8] for divergence form operators. As an application of this, a new approximation argument and known results we are able to extend the results in [10] for divergence form operators while obtaining totally new results for no...

We show that if γ is a curve in the unit disk, then arclength on γ is a Carleson measure iff the image of γ has finite length under every conformal map onto a domain with rectifiable boundary. Date: July 27, 2012. 1991 Mathematics Subject Classification. Primary: 30C62 Secondary:

We give a necessary and sufficient condition for a measure μ in the closed unit disk to be a reverse Carleson measure for Hardy spaces. This extends a previous result of Lefèvre, Li, Queffélec and Rodrı́guez-Piazza [LLQR]. We also provide a simple example showing that the analogue for the Paley-Wiener space does not hold. As it turns out the analogue never holds in any model space.

We define the weighted Carleson measure space CMO w using wavelets, where the weight function w belongs to the Muckenhoupt class. Then we show that CMO w is the dual space of the weighted Hardy space H p w by using sequence spaces. As an application, we give a wavelet characterization of BMOw.

We deal with some applications of Marcinkiewicz integrals to problems related to harmonic measure on the one hand, and to removability problems for Sobolev spaces and quasiconformal mappings on the other hand. Techniques of this type have been used by Carleson, Jones, Makarov, Smirnov... to address these problems, and as a general program to understand harmonic functions on complicated domains ...

Carleson and vanishing Carleson measures for Besov spaces on the unit ball of CN are defined using imbeddings into Lebesgue classes via radial derivatives. The measures, some of which are infinite, are characterized in terms of Berezin transforms and Bergman-metric balls, extending results for weighted Bergman spaces. Special cases pertain to Arveson and Dirichlet spaces, and a unified view wit...

We prove that if μ is a d-dimensional Ahlfors-David regular measure in R, then the boundedness of the d-dimensional Riesz transform in L(μ) implies that the non-BAUP David-Semmes cells form a Carleson family. Combined with earlier results of David and Semmes, this yields the uniform rectifiability of μ.

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|...