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Restriction Theorems for Anisotropically Homogeneous Hypersurfaces of

  • Elida Ferreyra and Marta Urciuolo
Published/Copyright: March 11, 2010
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Georgian Mathematical Journal
From the journal Volume 15 Issue 4

Abstract

For and Ξ²1, . . . , β𝑛 > 1 let be defined by , let 𝐡 be the open unit ball in and let βˆ‘ = {(π‘₯, Ο† (π‘₯)) : π‘₯ ∈ 𝐡}. For let 𝑅𝑓 : βˆ‘ β†’ β„‚ be defined by

where denotes the usual Fourier transform of 𝑓. Let Οƒ be the Borel measure on βˆ‘ defined by Οƒ (𝐴) = βˆ«π΅Ο‡π΄ (π‘₯, Ο† (π‘₯)) 𝑑π‘₯ and 𝐸 be the type set for the operator 𝑅, i.e. the set of pairs for which there exists 𝑐 > 0 such that for all . In this paper we obtain a polygonal domain contained in 𝐸. 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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