Georgia Institute of Technology College of Sciences

We show variational estimates for paraproducts, which can be viewed as bilinear generalizations of L\'epingle’s variational estimates for martingale averages or scaled families of convolution operators. The heart of the matter is the case of low variation exponents. Joint work with Camil Muscalu and Christoph Thiele.

We discuss a non-linear eigenvalue problem where the eigenvalue has a natural control-theoretic interpretation as an optimal "long-time averaged cost." We also show how such problems arise in financial market models with small transaction costs.

We start the proof of arXiv:1001.4043, which characterizes the two weight inequality for the Hilbert transform. This session will be devoted to necessity of the Poisson A_2 condition and the Energy Condition. Joint work with Ignacio Uriate-Tuero, and Eric Sawyer.

James Curry will continue his presentation of the paper  arXiv:0911.3437, which proves two-weight norm inequalities for a class of dyadic, positive operators.

Given a set of complex exponential e^{i \lambda_n x} how large do you have to take r so that the sequence is independent in L^2[-r,r] ? The answer is given in terms of the Beurling-Mallivan density.

This is the first meeting of a weekly working seminar on two weight inequalities in Harmonic Analysis. James Curry will present the paper arXiv:0911.3437, which proves two-weight norm inequalities for a class of dyadic, positive operators.

We are going to finish explaining the proof of Seip's Interpolation Theorem for the Bergman Space. This will be the last meeting of the seminar for the semester.

We are going to continue explaining the proof of Seip's Interpolation Theorem for the Bergman Space. We are going to demonstrate the sufficiency of these conditions for a certain example. We then will show how to deduce the full theorem with appropriate modifications of the example.

We are going to continue explaining the proof of Seip's Interpolation Theorem for the Bergman Space. We are going to demonstrate the sufficiency of these conditions for a certain example. We then will show how to deduce the full theorem with appropriate modifications of the example.

We continue our study of Seip's Interpolation Theorem in weighted Bergman spaces. This lecture should cover the necessary direction in the characterization of the Theorem.