David Beltran

Title: Regularity of fractional maximal functions

Abstract: It is known that fractional integrals and the classical fractional maximal function are smoothing operators, in the sense that they map Lebesgue spaces into first order Sobolev spaces. We will show that this phenomenon continues to hold for the fractional spherical maximal function when the dimension of the ambient space is greater than or equal to 5. Moreover, we will discuss some recent endpoint Sobolev bounds for classical fractional maximal functions, obtained with Fourier analytic techniques. This is joint work with João P. Ramos and Olli Saari.