Analysis and Probability Seminar

In this talk we will discuss a couple of boundedness theorems for oscillatory integral operators. Firstly, we study the weighted L^p boundedness of linear operators whose amplitudes do not have sufficient decay to allow for weighted boundedness for all A_p Muckenhoupt weights. In this situation we can obtain weighted L^p boundedness for a smaller class of Muckenhoupt weights. Secondly, we look at the boundedness of multilinear oscillatory integrals on local Hardy spaces. Here vector-valued inequalities allow us to study quasi-Banach spaces (where 0<p<1). This is a combination of joint work with Aksel Bergfeldt, Solange Mukeshimana, Salvador Rodriguez-Lopez and Wolfgang Staubach.