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Restriction Theorems for Anisotropically Homogeneous Hypersurfaces of
-
Elida Ferreyra
Published/Copyright:
March 11, 2010
Abstract
For and Ξ²1, . . . , Ξ²π > 1 let
be defined by
, let π΅ be the open unit ball in
and let β = {(π₯, Ο (π₯)) : π₯ β π΅}. For
let π
π : β β β be defined by
where denotes the usual Fourier transform of π. Let Ο be the Borel measure on β defined by Ο (π΄) = β«π΅Οπ΄ (π₯, Ο (π₯)) ππ₯ and πΈ be the type set for the operator π
, i.e. the set of pairs
for which there exists π > 0 such that
for all
. In this paper we obtain a polygonal domain contained in πΈ. We also give necessary conditions for a pair
. In some cases this result is sharp up to endpoints.
Key words and phrases:: Restriction theorems; Fourier transform
Received: 2006-06-23
Published Online: 2010-03-11
Published in Print: 2008-December
Β© Heldermann Verlag
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