#### Arbeitsgruppe Analysis und Partielle Differentialgleichungen

## S5B3: Regularity of maximal functions

#### Winter term 2017/18

### Organizers

### Schedule

#### Registration

Legally happens by signature before October 30. Additionally, the participants will also have to register technically via BASIS.#### Trial talks

Every participant should give a trial presentation to a lecturer or should extensively discuss the presentation with a lecturer at least one week before the official presentation.#### Written summary

Each participant is required to submit a short written summary of their topic in compliance with the module handbook.#### Talks

Starting from November 8, Wednesdays, 10-12, in seminar room 1.008.- Oct 25 Saari (Introduction)
- Nov 1 is a holiday
- Nov 8 Weigt (1)
- Nov 15 Weigt (8)
- Nov 22 Fraccaroli (3)
- Nov 29 Ramos (4)
- Dec 6 dies academicus
- Dec 13 Bilz (5)
- Dec 20 Bilz (5)
- Jan 10 He (7)
- Jan 17 He (6)
- Jan 24 Lappas (2)
- Jan 31 Lappas (2)

#### Grades

A grade for each talk is given immediately after the talk. Final grades also take into account the written summaries and participation in the other participants' talks and are given at the end of the lecture period.### Topics

Each participant will present 1 long or 2 short article(s) from the following list:- J. Kinnunen, The Hardy-Littlewood maximal function of a Sobolev function, Israel J. Math., 100 (1997), 117-124.
- E. Carneiro, R. Finder and M. Sousa, On the variation of maximal operators of convolution type II, (to appear in Rev. Mat. Iberoam.) (2015).
- J.M. Aldaz and J. Pérez Lázaro, Functions of bounded variation, the derivative of the one dimensional maximal function, and applications to inequalities, Trans. Amer. Math. Soc. 359 (2007), no. 5, 2443–2461.
- O. Kurka, On the variation of the Hardy-Littlewood maximal function, Ann. Acad. Sci. Fenn. Math. 40 (2015), no. 1, 109-133.
- H. Luiro, The variation of the maximal function of a radial function, 2017.
- J. Kinnunen and E. Saksman, Regularity of the fractional maximal function, Bull. London Math. Soc. 35 (2003), 529-535.
- S. Buckley, Is the maximal function of a Lipschitz function continous?, Ann. Acad. Sci. Fenn. Math. 24 (1999), no. 2, 519–528.
- H. Luiro, Continuity of the maximal operator in Sobolev spaces. Proc. Amer. Math. Soc. 135 (2007), no. 1, 243–251.

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