Pseudodifferential operators of mixed type adapted to distributions of k-planes

2013/11/01 by Elias M. Stein, Po-Lam Yung, Po‐Lam Yung +2
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations #math.AP #math.CA #math.CV

paper · pdf · doi:10.48550/arxiv.1311.0245

typos fixed

openalex publication_date 2013/11/01 · arxiv created 2014/12/11 · arxiv updated 2014/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the phenomena that arise when we combine the standard pseudodifferential operators with those operators that appear in the study of some sub-elliptic estimates, and on strongly pseudoconvex domains. The algebra of operators we introduce is geometrically invariant, and is adapted to a smooth distribution of tangent subspaces of constant rank. We isolate certain ideals in the algebra whose analysis is of particular interest.

Related

• Sub-Feller Semigroups Generated by Pseudodifferential Operators on Symmetric Spaces of Noncompact Type
• Pseudodifferentialoperatoren mit nichtglatten Koeffizienten auf Mannigfaltigkeiten
• Pseudodifferential operators on manifolds with scaled bounded geometry
• Pseudodifferential operators on manifolds with fibred corners
• On the relationship between the semiclassical and standard pseudodifferential algebras