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Sobolev and BV regularity for maximal operators

Emanuel Carneiro
Institution: 
ICTP
Location: 
A-133
Schedule: 
Thursday, May 23, 2019 - 14:00
Abstract: 

Consider the following innocent-looking question: can the (centered) one-dimensional Hardy-Littlewood maximal operator increase the total variation of a function? Surprisingly, this has been an open problem for almost two decades now. In this talk I will discuss some of the recent developments on the regularity theory for maximal operators, when acting on Sobolev or BV data. This is an active topic of research with several interesting open questions (like the one above). The talk should be accessible to a broad audience with a minimal background in Analysis.

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