Sets of p-restriction and p-spectral synthesis

Abstract

Abstract In this paper we investigate the restriction problem. More precisely, we give sufficient conditions for the failure of a set E in ℝ n to have the p-restriction property. We also extend the concept of spectral synthesis to Lp (ℝ n ) for sets of p-restriction when p > 1. We use our results to show that there are p-values for which the unit sphere is a set of p-spectral synthesis in ℝ n when n ⩾ 3.