Hardy and BMO spaces associated to divergence form elliptic operators

2006/11/27 by Steve Hofmann, Svitlana Mayboroda, Hofmann, Steve +1
Mathematics · #35J15 #42B25 #42B30 #42B35 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.math/0611804

openalex publication_date 2006/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider the second order divergence form elliptic operator L with complex bounded coefficients. In general, the operators related to it (such as Riesz transform or square function) lie beyond the scope of the Calderón-Zygmund theory. They need not be bounded in the classical Hardy, BMO and even some L^p spaces. In this work we generalize the classical approach and develop a theory of Hardy and BMO spaces associated to L, which includes, in particular, molecular decomposition, maximal function characterization, duality of Hardy and BMO spaces, John-Nirenberg inequality, and allows to handle aforementioned operators.

Citations

• On functions of bounded mean oscillation
• Some new function spaces and their applications to Harmonic analysis
• Hp spaces of several variables

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