Damped oscillatory integrals and boundedness of maximal operators associated to mixed homogeneous hypersurfaces

Details Damped oscillatory integrals and boundedness of maximal operators associated to mixed homogeneous hypersurfaces Damped oscillatory integrals and boundedness of maximal operators associated to mixed homogeneous hypersurfaces

2003-06-30

arxiv.org/abs/math/0306429v1

Mathematics

Classical Analysis and ODEs

16 pages

Scientific paper

We study the boundedness problem for maximal operators in 3-dimensional
Euclidean space associated to hypersurfaces given as the graph of $c+f$, where
$f$ is a mixed homogeneous function which is smooth away from the origin and
$c$ is a constant. Our result generalizes a corresponding theorem on mixed
homogeneous polynomial functions by A. Iosevich and E. Sawyer.

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