Mathematische Annalen

, Volume 344, Issue 1, pp 37–116

Hardy and BMO spaces associated to divergence form elliptic operators

Article

DOI: 10.1007/s00208-008-0295-3

Cite this article as:
Hofmann, S. & Mayboroda, S. Math. Ann. (2009) 344: 37. doi:10.1007/s00208-008-0295-3

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 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.

Mathematics Subject Classification (2000)

42B3042B3542B2535J15

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Missouri at ColumbiaColumbiaUSA
  2. 2.Department of MathematicsThe Ohio State UniversityColumbusUSA
  3. 3.Department of MathematicsPurdue UniversityW. LafayetteUSA