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CATEGORIES:Analysis Seminar
SUMMARY:Uniform Lp-improving for dilated averages over cur
ves - Jonathan Hickman (University of Edinburgh)
DTSTART:20141110T160000Z
DTEND:20141110T170000Z
UID:TALK1553AT
URL:/talk/index/1553
DESCRIPTION:Numerous authors have considered the problem of de
termining the Lebesgue space mapping properties of
the operator *A* given by convolution with
surface measure on some smooth curve in Euclidean
space. Essentially\, A takes averages over transl
ates of the curve. I will discuss a variant of thi
s problem where averages over both translates and
dilates of a fixed curve are considered. The sharp
range of estimates for the resulting operator is
obtained in all dimensions\, except for an endpoin
t. The techniques used are redolent of those previ
ously applied in the study of *A*. In parti
cular\, the arguments are based upon the refinemen
t method of Christ\, although significant adaptati
ons of this method are required to fully understan
d the additional smoothing afforded by averaging o
ver dilates. Some connections with weighted versio
ns of Fourier restriction inequalities will be des
cribed.
LOCATION:Physics West 106 (SR2)
CONTACT:José Cañizo
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