# FALL 2021 Nonlinear Analysis Seminar Series

### Date

2021年12月14日 (火) 10:00 11:00

Online via Zoom

### Title: Endpoint Sobolev regularity of the fractional maximal function

Abstract: Abstract: I will report some of the recent progress regarding the boundedness and continuity of the map $$f \mapsto |\nabla M_\beta f|$$ from the endpoint space $$W^{1,1}(\mathbb{R}^d)$$ to $$L^{d/(d-\beta)}(\mathbb{R}^d)$$, where $$M_\beta$$ denotes the fractional version of either the centered or uncentered Hardy--Littlewood maximal function. After contributions by several authors, the problem is now totally solved in an affirmative way. I will focus on my contributions, which correspond to the radial case (in joint work with J. Madrid), and also to the general case for the continuity of the map (in joint work with C. González-Riquelme, J. Madrid and J. Weigt). Please click here to register *After registering, you will receive a confirmation email containing information about joining the meeting.

###### Please click here to register *After registering, you will receive a confirmation email containing information about joining the meeting.
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