l^p decoupling for restricted k-broadness

To prove Fourier restriction estimate using polynomial partitioning, Guth introduced the concept of k-broad part of regular L ^p norm and obtained sharp k-broad restriction estimates. To go from k-broad estimates to regular L ^p estimates, Guth employed l ² decoupling result. In this article, similar to the technique introduced by Bourgain-Guth, we establish an analogue to go from regular L ^p norm to its (m+ 1) -broad part, as the error terms we have the restricted k-broad parts (k= 2 , … , m). To analyze the restricted k-broadness, we prove an l ^p decoupling result, which can be applied to handle the error terms and recover Guth’s linear restriction estimates.