|Location:||MSRI: Baker Board Room|
Title: Fefferman-Stein inequalities
Abstract: Given an operator T, we focus on obtaining two-weighted inequalities in which the weights are related via certain maximal function. These inequalites, which originated in work of Fefferman and Stein, have been established in an optimal way for different classical operators in Harmonic Analysis. In this talk, we survey some classical results and we present some recent Fefferman-Stein inequalities for pseudodifferential operators and for the solution operators to dispersive equations.
Title: Large Sets Avoiding Patterns ( joint work with Malabika Pramanik)
What conditions must be placed on a set E ⊂ Rn in order to guarantee that E contains certain finite arrangements of points? We will discuss some conditions on a set E that guarantee the existence of point configurations, and constructions of large sets E that avoid them. This work was completed jointly with Malabika Pramanik.
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