Sandra Pott

Applications of Laplace–Carleson embeddings to admissibility and controllability

It is shown how results on Carleson embeddings induced by the Laplace transform can be used to derive new and more general results concerning the weighted (infinite-time) admissibility of control and observation operators for linear semigroup systems with

Matrix weighted norm inequalities for commutators and paraproducts with matrix symbols

q

Endpoint compactness of singular integrals and perturbations of the Cauchy integral

-Riesz bases of eigenvectors. As an example, the heat equation is considered. Next, a new Carleson embedding result is proved, which gives further results on weighted admissibility for analytic semigroups. Finally, controllability by smoother inputs is characterized by means of a new result about weighted interpolation.

Thin sequences and their role in H-p theory, model spaces, and uniform algebras

Let B be a locally integrable matrix function, W a matrix Ap weight with 1<p<∞, and T be any of the Riesz transforms. We will characterize the boundedness of the commutator [T,B] on Lp(W) in terms of the membership of B in a natural matrix weighted BMO space. To do this, we will characterize the boundedness of dyadic paraproducts on Lp(W) via a new matrix weighted Carleson embedding theorem. Finally, we will use some of the ideas from these proofs to (among other things) obtain quantitative weighted norm inequalities for these operators and also use them to prove sharp L2 bounds for the Christ/Goldberg matrix weighted maximal function associated with matrix A2 weights.

Dyadic BMO on the bidisk

We prove sufficient and necessary conditions for the compactness of Calderon-Zygmund operators on the endpoint from L∞ (R) into CMO(R). We use this result to prove the compactness on Lp (R) with 1 < p < ∞ of a certain perturbation of the Cauchy integral on curves with normal derivatives satisfying a CMO-condition.

A T(1) theorem on product spaces

In this paper we revisit some facts about thin interpolating sequences in the unit disc from three perspectives: uniform algebras, model spaces, and

Sharp Bekolle estimates for the Bergman projection

H^p

On Laplace–Carleson embedding theorems

spaces. We extend the notion of asymptotic interpolation to

Weighted interpolation in Paley–Wiener spaces and finite-time controllability

H^p

Sarason Conjecture on the Bergman Space

spaces, for