Caltech/UCLA Joint Analysis Seminar

The regularity of maximal operators has been a topic of interest in harmonic analysis over the past decades. In this topic we are interested in what can be said about the variation of a maximal function Mf given some information about the original function f. In this talk we present some recent results about the continuity of the map f↦ ∇Mf for the uncentered Hardy-Littlewood maximal operator in both the BV(ℝ) and the W1,1rad(ℝd) settings.

This is based on joint works with D. Kosz (BV case) and E. Carneiro and J. Madrid (radial case)