RESTRICTED AVERAGING OPERATORS IN THE FINITE FIELD SETTING

Abstract

In this paper we study the mapping properties of the finite field restricted averaging operators to various algebraic varieties. We derive necessary conditions for the boundedness of the generalized restricted averaging operator related to arbitrary algebraic varieties. It is shown that the necessary conditions are in fact sufficient in the specific case when the Fourier transform on varieties has enough decay estimates. Our work extends the known optimal result on regular varieties such as paraboloids and spheres to certain lower dimensional varieties.

This article was migrated from the previous system via automation. The abstract may not be written correctly. Please view the PDF file.