Tohoku Mathematical Journal
2014

June
SECOND SERIES VOL. 66, NO. 2

Tohoku Math. J.
66 (2014), 269-287

Title FUNCTIONS OF VANISHING MEAN OSCILLATION ASSOCIATED TO NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING DAVIES-GAFFNEY ESTIMATES

Author The Anh Bui

(Received October 26, 2011, revised May 28, 2013)
Abstract. Let $L$ be a nonnegative self-adjoint operator satisfying Davies-Gaffney estimates on $L^2(X)$, where $X$ is a metric space. In this paper, we introduce and develop a new function space VMO$_{L}(X)$ of vanishing mean oscillation type associated to $L$. We then prove that the dual of VMO$_{L}(X)$ is the Hardy space $H_L(X)$ which was investigated in [18]. Some characterizations of VMO$_{L}(X)$ are also established.

Mathematics Subject Classification. Primary 42B20; Secondary 42B25.

Key words and phrases. Non-negative self-adjoint operator, Hardy space, BMO, VMO, space of homogeneous type.

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