Joint BCAM-UPV/EHU Analysis and PDE seminar: Weak type Gagliardo seminorms via maximal inequalities

Abstract

The celebrated Bourgain-Brezis-Mironescu formula enables us to recover Sobolev spaces in terms of limits of Gagliardo seminorms. Very recently, Brezis, Van Schaftingen and Yung have proposed an alternative methodology to approach Sobolev spaces via limits of weak-type Gagliardo functionals. In this talk we will show that the BvSY result is a special case of a more general phenomenon based on maximal inequalities and sequences of operators. In particular, we shall derive not only analogs of the BvSY theorem for different kinds of function spaces (Lebesgue, Calderon, higher-order Sobolev), but also applications to the PDE's, ergodic theory, Fourier series, etc This is joint work with Mario Milman.

Link to the session: https://zoom.us/j/95033836050?pwd=UExQT1lLU09PTHNzdmNWdzdQbTEyZz09

More info at https://sites.google.com/view/apdebilbao/home