Multiparameter Maximal Functions Along Dilation-Invariant Hypersurfaces

Hasse Carlsson, Peter Sjogren, Jan-Olov Stromberg
1985 Transactions of the American Mathematical Society  
Consider the hypersurface xn+i = Fli XV in Rn+1-The associated maximal function operator is defined as the supremum of means taken over those parts of the surface lying above the rectangles {0 < ij < hj, i = \,...,n). We prove that this operator is bounded on IP for p > 1. An analogous result is proved for a quadratic surface in R3.
doi:10.2307/2000183 fatcat:xy73hlyc6jfdvbiirvkfilvu3u