Multilinear Integral Operators: Classic, Curved, and Discrete

Dong Dong
University of Illinois at Urbana-Champaign
Graduate Student

“Several important integral operators in harmonic analysis will be presented in an  organized way. The fundamental question about these operators is the boundedness on Lebesgue spaces. We will show that the difficulty to establish the boundedness will change dramatically once we move from the classic type of operators to their curved and discrete analogs. We will also survey some useful techniques in the study of these operators. It is very interesting to see that harmonic analysis can interact with many other fields of mathematics such as PDE, ergodic theory, number theory, combinatorics, and even algebraic geometry”.