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SUMMARY:George Dosidis (Charles University)
DTSTART:20210215T170000Z
DTEND:20210215T175000Z
DTSTAMP:20260423T010458Z
UID:anpdews/50
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/anpdews/50/"
 >The uncentered spherical maximal function and Nikodym sets</a>\nby George
  Dosidis (Charles University) as part of HA-GMT-PDE Seminar\n\n\nAbstract\
 nStein's spherical maximal function is an analogue of the Hardy-Littlewood
  maximal function\, where the averages are taken over spheres instead of b
 alls. While the uncentered Hardy-Littlewood maximal function is bounded on
  Lp for all p>1 and pointwise equivalent to its centered counterpart\, the
  corresponding uncentered spherical maximal function is not as well-behave
 d.\n\nWe provide multidimensional versions of the Kakeya\, Nikodym\,and Be
 sicovitch constructions associated with spheres. These yield counterexampl
 es indicating that maximal operators given by translations of spherical av
 erages are unbounded on Lp for all finite p.\n\nHowever\, for lower-dimens
 ional sets of translations\, we obtain Lp boundedness for the associated m
 aximally translated spherical averages for a certain range of p that\ndepe
 nds on the Minkowski dimension of the set of translations. This is joint w
 ork with A. Chang and J. Kim.\n
LOCATION:https://researchseminars.org/talk/anpdews/50/
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