Operator estimates and elliptic regularity

Abstract

In order to make use of the symbol smoothing of §1.3, we need operator estimates on p(x, D) when p(x, ξ) ∈C^sS ^m_{1, δ} . We give a number of such results in §2.1, most of them following from work of Bourdaud [BG]. The main result, Theorem 2.1.A, treats the case δ = 1. This will be very useful for the treatment of paradifferential operators in Chapter 3.