Instructor: Loukas Grafakos

Description: In the first weeks of the semester we will discuss elements from the theory of weighted norm inequalities and extrapolation of operators. The class of weights we will consider is A_p.

We will then focus on the boundedness and convergence of Fourier series and integrals in one and higher
dimensions. Emphasis will be given to norm convergence of certain means of partial Fourier integrals (such as the Bochner Riesz means) and the almost everywhere of Fourier series of L^p functions (p>1) in dimension one.

We will use weighted inequalities to obtain the almost everywhere convergence of Bochner-Riesz means of L^p functions in the optimal range of parameters for values of p>2.