This is an announcement for the paper "A universal $H_1$-BMO duality theory for semigroups of operators" by Tao Mei.

Abstract: Let (M,\mu) be a sigma-finite measure space. Let (T_t) be a semigroup of positive preserving maps on (M,\mu) with standard assumptions. We prove a $H_1$-BMO duality theory with assumptions only on the semigroup of operators. The H1's are defined by square functions of P. A. Meyer's gradient form. The formulation of the assumptions does not rely on any geometric/metric property of M nor on the kernel of the semigroups of operators. Our main results extend to the noncommutative setting as well, e.g. the case where $L_\infty(M,\mu)$ is replaced by von Neuman algebras with a semifinite trace. We also prove a Carlson embedding theorem for semigroups of operators.

Archive classification: math.CA math.FA math.OA

Mathematics Subject Classification: 46L51 42B25 46L10 47D06

Remarks: 22 pages

Submitted from: mei@wayne.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1005.4424

or

http://arXiv.org/abs/1005.4424