Tent Spaces Associated with Semigroups of Operators

Details Tent Spaces Associated with Semigroups of Operators Tent Spaces Associated with Semigroups of Operators

2007-09-26

arxiv.org/abs/0709.4226v4

Journal of Functional Analysis, 255 (2008) 3356-3406

Mathematics

Functional Analysis

The statement of Lemma 3.11 is corrected

Scientific paper

We study tent spaces on general measure spaces $(\Omega, \mu)$. We assume that there exists a semigroup of positive operators on $L^p(\Omega, \mu)$ satisfying a monotone property but do not assume any geometric/metric structure on $\Omega$. The semigroup plays the same role as integrals on cones and cubes in Euclidean spaces. We then study BMO spaces on general measure spaces and get an analogue of Fefferman's $H^1$-BMO duality theory. We also get a $H^1$-BMO duality inequality without assuming the monotone property. All the results are proved in a more general setting, namely for noncommutative $L^p$ spaces.

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