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