# Boundedness of Fourier integral operators on Fourier Lebesgue spaces and affine fibrations

Studia Mathematica (2010)

- Volume: 198, Issue: 3, page 207-219
- ISSN: 0039-3223

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topFabio Nicola. "Boundedness of Fourier integral operators on Fourier Lebesgue spaces and affine fibrations." Studia Mathematica 198.3 (2010): 207-219. <http://eudml.org/doc/285591>.

@article{FabioNicola2010,

abstract = {We study Fourier integral operators of Hörmander’s type acting on the spaces $ℱL^\{p\}(ℝ^\{d\})_\{comp\}$, 1 ≤ p ≤ ∞, of compactly supported distributions whose Fourier transform is in $L^\{p\}$. We show that the sharp loss of derivatives for such an operator to be bounded on these spaces is related to the rank r of the Hessian of the phase Φ(x,η) with respect to the space variables x. Indeed, we show that operators of order m = -r|1/2-1/p| are bounded on $ℱ L^\{p\}(ℝ^\{d\})_\{comp\}$ if the mapping $x ↦ ∇_\{x\}Φ(x,η)$ is constant on the fibres, of codimension r, of an affine fibration.},

author = {Fabio Nicola},

journal = {Studia Mathematica},

language = {eng},

number = {3},

pages = {207-219},

title = {Boundedness of Fourier integral operators on Fourier Lebesgue spaces and affine fibrations},

url = {http://eudml.org/doc/285591},

volume = {198},

year = {2010},

}

TY - JOUR

AU - Fabio Nicola

TI - Boundedness of Fourier integral operators on Fourier Lebesgue spaces and affine fibrations

JO - Studia Mathematica

PY - 2010

VL - 198

IS - 3

SP - 207

EP - 219

AB - We study Fourier integral operators of Hörmander’s type acting on the spaces $ℱL^{p}(ℝ^{d})_{comp}$, 1 ≤ p ≤ ∞, of compactly supported distributions whose Fourier transform is in $L^{p}$. We show that the sharp loss of derivatives for such an operator to be bounded on these spaces is related to the rank r of the Hessian of the phase Φ(x,η) with respect to the space variables x. Indeed, we show that operators of order m = -r|1/2-1/p| are bounded on $ℱ L^{p}(ℝ^{d})_{comp}$ if the mapping $x ↦ ∇_{x}Φ(x,η)$ is constant on the fibres, of codimension r, of an affine fibration.

LA - eng

UR - http://eudml.org/doc/285591

ER -

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