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PRODID:-//talks.bham.ac.uk//v3//EN
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CATEGORIES:Analysis Seminar
SUMMARY:Some sharp restriction inequalities - Diogo Olivei
ra e Silva (University of Bonn)
DTSTART:20141204T160000Z
DTEND:20141204T170000Z
UID:TALK1567AT
URL:/talk/index/1567
DESCRIPTION:The goal of this talk will be to find the sharp fo
rms and characterize the complex-valued extremizer
s of the adjoint Fourier restriction inequalities
on the sphere:\n‖ℱ(*f* σ)‖_{Lp(ℝd)} ≲ ‖f‖_{Lq(Sd-1\, σ)}~~\, in the cases ~~*(d\,p\,
q) = (d\,2k\, q)* with *d\,k ∈ ℕ* and <
em>q ∈ ℝ^{+} ∪ {∞} satisfying: \n\n(a
) *k = 2*\, *q ≥ 2* and *3 ≤ d ≤
7*\;\n

\n(b) *k = 2*\, *q ≥ 4 and **d ≥ 8*\;

\n(c) *k ≥ 3*\,
*q ≥ 2k* and *d ≥ 2*. \n\nTools inc
lude a spherical harmonic decomposition\, the stud
y of the Cauchy-Pexider functional equation for su
msets of the sphere\, and a sharp multilinear weig
hted restriction inequality with weight related to
the *k*-fold convolution of the surface me
asure. \nThis topic builds up on recent results by
D. Foschi\, and is joint work with E. Carneiro.\n
LOCATION:Watson 310
CONTACT:José Cañizo
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