Hardy and BMO spaces associated to divergence form elliptic operators
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- Hofmann, S. & Mayboroda, S. Math. Ann. (2009) 344: 37. doi:10.1007/s00208-008-0295-3
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Consider a second order divergence form elliptic operator L with complex bounded measurable coefficients. In general, operators based on L, such as the Riesz transform or square function, may lie beyond the scope of the Calderón–Zygmund theory. They need not be bounded in the classical Hardy, BMO and even some Lp spaces. In this work we develop a theory of Hardy and BMO spaces associated to L, which includes, in particular, a molecular decomposition, maximal and square function characterizations, duality of Hardy and BMO spaces, and a John–Nirenberg inequality.