#
Sparse domination of singular integral operators

October 9 to October 13, 2017
at the

American Institute of Mathematics,
San Jose, California

organized by

Amalia Culiuc,
Francesco Di Plinio,
and Yumeng Ou

## Original Announcement

This workshop 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.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop: