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boundedness of integral operators with oscillatory kernels: linear versus quadratic phases
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Abstract
Let be the oscillatory integral operators defined by
where
is the unit ball in
and
We compare the asymptotic behaviour as
of the operator norms
for all
We prove that, except for the dimension
this asymptotic behaviour depends on the linearity or quadraticity of the phase in s only. We are led to this problem by an observation on inhomogeneous Strichartz estimates for the Schrödinger equation.
Notes
No potential conflict of interest was reported by the authors.