Algebras of singular integral operators with kernels controlled by multiple norms

2015/11/18 by Alexander Nagel, Nagel, Alexander, Fulvio Ricci +5
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1511.05702

arxiv created 2015/11/18 · arxiv updated 2015/11/19

Abstract

The purpose of this paper is to study algebras of singular integral operators on ℝⁿ and nilpotent Lie groups that arise when one considers the composition of Calderón-Zygmund operators with different homogeneities, such as operators that occur in sub-elliptic problems and those arising in elliptic problems. For example, one would like to describe the algebras containing the operators related to the Kohn-Laplacian for appropriate domains, or those related to inverses of Hörmander sub-Laplacians, when these are composed with the more standard class of pseudo-differential operators. The algebras we study can be characterized in a number of different but equivalent ways, and consist of operators that are pseudo-local and bounded on L^p for 1<p<∞. While the usual class of Calderón-Zygmund operators is invariant under a one-parameter family of dilations, the operators we study fall outside this class, and reflect a multi-parameter structure.

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