Title: On Derivative Bounds for Maximal Functions.
Abstract: We will talk about the regularity properties of maximal operators acting on BV-functions and W^{1,1}-functions. In this poster, we will be presenting recent results about new bounds for the derivative of the fractional maximal function, both in the continuous and in the discrete settings. Moreover, we will present sharp inequalities for the variation of the discrete maximal operator.
This presentation will be based on the following works:
Paper 1: http://arxiv.org/abs/1510.02965 (To appear in Transactions of the American Mathematical Society)
Paper 2: http://arxiv.org/abs/1512.04112 (Preprint)