Multiparameter Maximal Functions Along Dilation-Invariant Hypersurfaces

摘要

The maximal function operator associated to the equation of a hypersurface is defined. That this operator is bounded on L sup p spaces is proved. This boundedness is established by one-dimensional maximal functions. Methods for maximal function along curves, involving Fourier transformation and analytic interpolation are used. An analogous result for a quadratic surface is proved.