Let L be the infinitesimal generator of an analytic semigroup on L²(ℝⁿ) with suitable upper bounds on its heat kernels. Auscher, Duong, and McIntosh defined a Hardy space H¹L by means of an area integral function associated with the operator L. By using a variant of the maximal function associated with the semigroup [equation omitted for formatting reasons], a space BMO L of functions of BMO type was defined by Duong and Yan and it generalizes the classical BMO space. In this paper, we show that if L has a bounded holomorphic functional calculus on L²(ℝⁿ), then the dual space of H¹L is BMO L* where L* is the adjoint operator of L. We then obtain a characterization of the space BMO L in terms of the Carleson measure. We also discuss the dimensions of the kernel spaces KL of BMO L when L is a second-order elliptic operator of divergence form and when L is a Schrödinger operator, and study the inclusion between the classical BMO space and BMO L spaces associated with operators.
Copyright 2005 American Mathematical Society. First published in Journal of the American Mathematical Society, Volume 18, Issue 4, published by the American Mathematical Society. The original article can be found at http://dx.doi.org/10.1090/S0894-0347-05-00496-0.