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SUMMARY:Tainara Borges (Brown University)
DTSTART:20240416T180000Z
DTEND:20240416T190000Z
DTSTAMP:20260423T024552Z
UID:OARS/57
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OARS/57/">So
 bolev smoothing estimates for bilinear maximal operators with fractal dila
 tion sets</a>\nby Tainara Borges (Brown University) as part of OARS Online
  Analysis Research Seminar\n\n\nAbstract\nGiven a hypersurface $S\\subset 
 \\mathbb{R}^{2d}$\, we study the bilinear averaging operator that averages
  a pair of functions over S\, as well as more general bilinear multipliers
  of limited decay and various maximal analogs. Of particular interest are 
 bilinear maximal operators associated to a fractal dilation set $E\\subset
  [1\,2]$\; in this case\, the boundedness region of the maximal operator i
 s associated to the geometry of the hypersurface and various notions of th
 e dimension of the dilation set. In particular\, we determine Sobolev smoo
 thing estimates at the exponent $L^{2}\\times L^{2}\\rightarrow L^2$ using
  Fourier-analytic methods\, which allow us to deduce additional $L^{p}$ im
 proving bounds for the operators and sparse bounds and their weighted coro
 llaries for the associated multi-scale maximal functions. We also extend t
 he method to study analogues of these questions for the triangle averaging
  operator and biparameter averaging operators. In addition\, some necessar
 y conditions for boundedness of these operators are obtained.\n
LOCATION:https://researchseminars.org/talk/OARS/57/
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