Closed Range Estimates for (partial derivative)over-bar(b) on CR Manifolds of Hypersurface Type

Author(s)

Coacalle, Joel ^[1] ; Raich, Andrew ^[2]

Affiliation

^[1] Univ Fed Sao Carlos, Dept Matemat, Rodovia Washington Luis, Km 235, Caixa Postal 676, Sao Carlos - Brazil

^[2] 1 Univ Arkansas, SCEN 327, Fayetteville, AR 72701 - USA

• Document type: Journal article
• Source: JOURNAL OF GEOMETRIC ANALYSIS; v. 31, n. 1, p. 366-394, JAN 2021.
• Web of Science Citations: 1

Abstract

The purpose of this paper is to establish sufficient conditions for closed range estimates on (0, q)-forms, for some fixedq, 1 <= q <= n-1, for (partial derivative) over bar (b) in both L-2 and L-2-Sobolev spaces in embedded, not necessarily pseudoconvex CR manifolds of hypersurface type. The condition, named weak Y(q), is both more general than previously established sufficient conditions and easier to check. Applications of our estimates include estimates for the Szego projection as well as an argument that the harmonic forms have the same regularity as the complex Green operator. We use a microlocal argument and carefully construct a norm that is well suited for a microlocal decomposition of form. We do not require that the CR manifold is the boundary of a domain. Finally, we provide an example that demonstrates that weak Y(q) is an easier condition to verify than earlier, less general conditions. (AU)

• FAPESP's process: 18/02663-0 - Global ultradifferentiable functions, complex analysis, and PDE's
• Grantee: Gustavo Hoepfner
• Support Opportunities: Research Grants - Visiting Researcher Grant - International