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

Research paper by I. A. Ikromov, M. Kempe, D. Mueller

Indexed on: 30 Jun '03Published on: 30 Jun '03Published in: Mathematics - Classical Analysis and ODEs


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.