for this workshop
Sparse domination of singular integral operators
American Institute of Mathematics, San Jose, California
Amalia Culiuc, Francesco Di Plinio, and Yumeng Ou
This workshop, sponsored by AIM and the NSF, will be devoted to sparse domination of singular integral operators and to its applications in harmonic analysis, partial differential equations, ergodic theory, and other related fields.
The concept of dominating singular integral operators, which are a priori non-local and non-positive, by sparse operators, which are positive sums of local averages, originated in the work of Lerner (2013) as an alternative route to Hytonen's A2 theorem (2012). Since then, sparse domination has become a leading technique not only within Calderon-Zygmund theory, but also in contexts extending well beyond, such as the study of semigroups of operators, Bochner-Riesz type multipliers, matrix-kerneled and nonhomogeneous singular integrals, oscillatory and arithmetic singular integrals, and modulation invariant multilinear singular integrals. For all such classes of operators, sparse estimates have given rise to new weighted bounds, as well as a wealth of open questions and further directions.
It is tempting to conjecture that suitable sparse theorems hold for all operators that are quasi-local, in the sense that at points far away from the support of the input function, the operator is well approximated by maximal averages. This workshop is designed with the intent of bringing together experts in sparse domination for singular integrals with leading specialists in areas where this principle and its consequences could be further explored.
The main topics for the workshop are
- Sharp sparse domination of rough singular integrals, oscillatory integrals, Radon transforms, Bochner-Riesz multipliers.
- Sharp sparse domination of singular integrals in the nonhomogeneous setting.
- A sparse domination principle for multiparameter singular integrals.
- Sparse domination of modulation invariant singular integrals.
- Sparse domination of oscillatory integrals and Radon-type transforms over the integers.
- A multilinear weighted theory for positive sparse forms and a suitable related extrapolation theory.
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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