American Institute of Mathematics, San Jose, California
Amalia Culiuc, Francesco Di Plinio, and Yumeng Ou
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
The workshop schedule.
A report on the workshop activities.
A list of open problems.
Papers arising from the workshop: