# Restriction theorems for the Fourier transform to homogeneous polynomial surfaces in ℝ³

E. Ferreyra; T. Godoy; M. Urciuolo

Studia Mathematica (2004)

- Volume: 160, Issue: 3, page 249-265
- ISSN: 0039-3223

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topE. Ferreyra, T. Godoy, and M. Urciuolo. "Restriction theorems for the Fourier transform to homogeneous polynomial surfaces in ℝ³." Studia Mathematica 160.3 (2004): 249-265. <http://eudml.org/doc/284895>.

@article{E2004,

abstract = {Let φ:ℝ² → ℝ be a homogeneous polynomial function of degree m ≥ 2, let Σ = (x,φ(x)): |x| ≤ 1 and let σ be the Borel measure on Σ defined by $σ(A) = ∫_\{B\} χ_\{A\}(x,φ(x))dx$ where B is the unit open ball in ℝ² and dx denotes the Lebesgue measure on ℝ². We show that the composition of the Fourier transform in ℝ³ followed by restriction to Σ defines a bounded operator from $L^\{p\}(ℝ³)$ to $L^\{q\}(Σ,dσ)$ for certain p,q. For m ≥ 6 the results are sharp except for some border points.},

author = {E. Ferreyra, T. Godoy, M. Urciuolo},

journal = {Studia Mathematica},

keywords = {restriction theorems; Fourier transform; Littlewood-Paley decomposition; Littlewood-Paley inequality},

language = {eng},

number = {3},

pages = {249-265},

title = {Restriction theorems for the Fourier transform to homogeneous polynomial surfaces in ℝ³},

url = {http://eudml.org/doc/284895},

volume = {160},

year = {2004},

}

TY - JOUR

AU - E. Ferreyra

AU - T. Godoy

AU - M. Urciuolo

TI - Restriction theorems for the Fourier transform to homogeneous polynomial surfaces in ℝ³

JO - Studia Mathematica

PY - 2004

VL - 160

IS - 3

SP - 249

EP - 265

AB - Let φ:ℝ² → ℝ be a homogeneous polynomial function of degree m ≥ 2, let Σ = (x,φ(x)): |x| ≤ 1 and let σ be the Borel measure on Σ defined by $σ(A) = ∫_{B} χ_{A}(x,φ(x))dx$ where B is the unit open ball in ℝ² and dx denotes the Lebesgue measure on ℝ². We show that the composition of the Fourier transform in ℝ³ followed by restriction to Σ defines a bounded operator from $L^{p}(ℝ³)$ to $L^{q}(Σ,dσ)$ for certain p,q. For m ≥ 6 the results are sharp except for some border points.

LA - eng

KW - restriction theorems; Fourier transform; Littlewood-Paley decomposition; Littlewood-Paley inequality

UR - http://eudml.org/doc/284895

ER -

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