Hardy and BMO spaces associated to divergence form elliptic operators |
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Authors: | Steve Hofmann Svitlana Mayboroda |
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Institution: | (1) Department of Mathematics, University of Missouri at Columbia, Columbia, MO 65211, USA;(2) Department of Mathematics, The Ohio State University, 231 W 18th Avenue, Columbus, OH 43210, USA;(3) Present address: Department of Mathematics, Purdue University, W. Lafayette, IN 47907-2067, USA |
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Abstract: | 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 L
p
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.
S. Hofmann was supported by the National Science Foundation. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 42B30 42B35 42B25 35J15 |
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