for this workshop
Carleson theorems and multilinear operators
American Institute of Mathematics, San Jose, California
Philip Gressman, Victor Lie, Lillian Pierce, and Po Lam Yung
This workshop, sponsored by AIM and the NSF, will be devoted to a selection of questions at the intersection of Carleson operators and multilinear operators, with an aim of bringing together a group of established experts and young researchers in order to facilitate the exchange of ideas and open the perspective of collaborative work on a set of core problems.
A celebrated theorem of Carleson (1966) states that the Fourier series of any $L^2$ function on the unit circle converges almost everywhere. This result, as extended by Hunt (1968) and Sjolin (1971), can also be stated in terms of the $L^p$ boundedness of a certain maximal operator involving both oscillatory and singular behavior, now known as the Carleson operator. The ideas at the heart of Carleson's method were substantially enriched by the different perspective of C. Fefferman (1973). These two combined approaches later proved to be influential in the seminal work of Lacey and Thiele on the boundedness of the Bilinear Hilbert Transform (1997/1999).
Ultimately, this circle of ideas and methods developed into a new field of mathematics now known as time-frequency analysis. By now, time-frequency has established direct connections with a number of different areas of mathematics such as ergodic theory, scattering theory and maximal multilinear operators. More recently, in a less direct way, further connections were established with other areas, among which we mention additive combinatorics, geometric measure theory, geometric incidence, and algebraic topology.
The main topics for the workshop are:
- The polynomial Carleson operator, and its variants, with particular attention to the possibility of approaching higher dimensional problems
- The Hilbert transform along vector fields
- Multilinear singular integrals
- Multilinear oscillatory integrals
The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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