In this paper, norm estimates are obtained for the problem of minimal-norm tangential interpolation by vector-valued analytic functions in weighted H spaces, expressed in terms of the Carleson constants of related scalar measures. Applications are given to the notion of p-controllability properties of linear semigroup systems and controllability by functions in certain Sobolev spaces.

In this note we present a different approach to the A∞ extrapolation via Carleson measures developed in [HM] and we illustrate the use of this technique by reproving a well known result of [FKP]. The AMSI-ANU Workshop on Spectral Theory and Harmonic Analysis ANU, Canberra, 13--17 July, 2009 Proceedings of the Centre for Mathematics and its Applications 44 (2010), 143--166.

We present conditions on families of diffeomorphisms that guarantee statistical stability and SRB entropy continuity. They rely on the existence of horseshoe-like sets with infinitely many branches and variable return times. As an application we consider the family of Hénon maps within the set of Benedicks-Carleson parameters.

We prove that Jacobi, CMV, and Schrödinger operators, which are reflectionless on a homogeneous set E (in the sense of Carleson), under the assumption of a Blaschke-type condition on their discrete spectra accumulating at E, have purely absolutely continuous spectrum on E.

We consider here the so called s-Carleson measures with additive logarithmic terms in the unit disc, when 0 < s < 1 and we give many equivalent definitions. As applications, we characterize the pointwise multipliers on Qs and on its logarithmic counterpart Qs,log. Boundedness of the Cesaro operator on Qs and from Qs,log to Qs is considered as well.

We construct extensions of Varopolous type for functions f ∈ BMO ( E ) , any uniformly rectifiable set codimension one. More precisely, let Ω ⊂ R n + 1 be an open satisfying the corkscrew condition, with -dimensional boundary ∂Ω, and σ ≔ H ⌊ ∂ denote surface measure on ∂Ω. show that if d compact support then there exists a smooth function V in such | ∇ Y is Carleson norm controlled by converges...