Bounded holomorphic functional calculus for non-divergence form differential operators. (English) Zbl 1020.47033

Duong, Xuan Thinh; Yan, Li Xin

Differ. Integral Equ. 15, No. 6, 709-730 (2002).

From the authors’ abstract: “Let \(L\) be a second-order elliptic partial differential operator of non-divergence form acting on \(\mathbb{R}^n\) with bounded coefficients. We show that for each \(1<p_0<2\), \(L\) has a bounded \(H_\infty\)-functional calculus on \(L^p(\mathbb{R}^n)\) for \(p_0<p <\infty\) if the BMO norm of the coefficients is sufficiently small”.

Reviewer: Niels Jacob (Swansea)

MSC:

47F05	General theory of partial differential operators
35J15	Second-order elliptic equations
42B20	Singular and oscillatory integrals (Calderón-Zygmund, etc.)
47A60	Functional calculus for linear operators

Keywords:

second-order elliptic operators; \(H_\infty\)-calculus; BMO norm