J. CARLESON, 1'2 P. ALSTERGREN, 2 A. APPELGREN, 2 B. APPELGREN, 2 S. KOPP, 2 G. R. SRINIVASAN, 4 E. THEODORSSON 4 and T. LUNDEBERG 1'3'* ~Department of Physiology and Pharmacology, Division of Physiology II, S-171 77, Stockholm, Sweden, 2Center for Clinical Oral Science, School of Dentistry, Karolinska Institutet, Box 4064, S-141 04, Huddinge, Sweden, 3Nociceptive Pain Unit, Department of Rehab...

We give an alternative proof of the Benedicks-Carleson theorem on the existence of strange attractors in Hénon-like maps in the plane. To bypass a huge inductive argument, we introduce an induction-free explicit definition of dynamically critical points. The argument is sufficiently general and in particular applies to the case of non-invertible maps as well. It naturally raises the question of...

We prove that the generalized Carleson operator Cd with polynomial phase function is of strong type (p, r), 1 < r < p < ∞; this yields a positive answer in the 1 < p < 2 case to a conjecture of Stein which asserts that for 1 < p < ∞ we have that Cd is of strong type (p, p). A key ingredient in this proof is the further extension of the relational time-frequency perspective (introduced in [5]) t...

Let Ω be a bounded C∞-smoothly bounded domain in C. For such a domain we define a new notion between strict pseudo-convexity and pseudo-convexity: the size of the set W of weakly pseudo-convex points on ∂Ω is small with respect to Minkowski dimension: near each point in the boundary ∂Ω, there is at least one complex tangent direction in which the slices of W has a upper Minkowski dimension stri...

Let Ω be a bounded C∞-smoothly bounded domain in C. For such a domain we define a new notion between strict pseudo-convexity and pseudo-convexity: the size of the set W of weakly pseudo-convex points on ∂Ω is small with respect to Minkowski dimension: near each point in the boundary ∂Ω, there is at least one complex tangent direction in which the slices of W has a upper Minkowski dimension stri...

The problem to estimate expressions of the kind \( Y\left(\lambda \right)=\underset{x\upepsilon \left[0,1\right]}{\sup}\left|\underset{0}{\overset{x}{\int }}f(t){e}^{i\lambda t} dt\right| \) is considered. In particular, for case f ∈ Lp[0, 1], p (1, 2], we prove {\left\Vert \right)\right\Vert}_{L_q\left(\mathbb{R}\right)}\le C{\left\Vert f\right\Vert}_{L_p} each q exceeding p', where 1/p+1/p' =...

We prove an analogue of a perturbation result for the Dirichlet problem divergence form elliptic operators by Fefferman, Kenig and Pipher, degenerate David, Feneuil Mayboroda, which were developed to study geometric analytic properties sets with boundaries whose co-dimension is higher than 1. These are ? div A ? , where weighted matrix crafted weigh distance high boundary in way that allows nou...

This paper studies Volterra evolution equations from the point of view of control theory, in the case that the generator of the underlying semigroup has a Riesz basis of eigenvectors. Conditions for admissibility of the system’s control operator are given in terms of the Carleson embedding properties of certain discrete measures. Moreover, exact and null controllability are expressed in terms o...

We consider a basic d-adic model for the scattering transform on the line. We prove L bounds for this scattering transform and a weak L bound for a Carleson type maximal operator (Theorem 1.4). The latter implies boundedness of d-adic models of generalized eigenfunctions of Dirac type operators with potential in L(IR). We show that this result cannot be obtained by estimating the terms in the n...

We prove that the multiplier algebra of the Drury-Arveson Hardy space H n on the unit ball in C n has no corona in its maximal ideal space, thus generalizing the famous Corona Theorem of L. Carleson in the unit disk. This result is obtained as a corollary of the Toeplitz Corona Theorem and a new Banach space result: the Besov-Sobolev space B p has the ”baby corona property” for all 0 ≤ σ < n p ...