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Real-variable theory of (Musielak-)Orlicz-Hardy spaces associated with differential operators and its applications

As is well-known, because of their important applications in several branches of mathematics, such as harmonic analysis and partial differential equations, the theory of Calderon-Zygmund singular integral operators and the real-variable theory of various function spaces, which could characterize the boundedness of those operators, turn into one of the main contents of modern harmonic analysis. However, the real-variable theory of classical function spaces has been no longer suitable for characterizing the boundedness of singular integral operators associated with some more general differential operators than Laplace operators. Thus, for different operators, it has become one of the very active research fields of harmonic analysis in recent years to develop the real-variable theory of function spaces, which are suitable to those operators and could characterize the boundedness of singular integral operators associated with those operators. In this article, we study the realvariable theory of (Musielak-)Orlicz-Hardy spaces associated with some differential operators, including secondorder divergence form elliptic operators and Schrodinger operators as special cases, on n -dimensional Euclidean space R n , strongly domains of R n or metric spaces with doubling measure, and its applications to the boundedness of operators.