Shao Xiong-HOU, Da Chun-YANG, Si Bei-YANG
Let
X be a space of homogenous type and
φ; :
X ×[0,∞) → [0,∞) be a growth function such that
φ;(·,
t) is a Muckenhoupt weight uniformly in
t and
φ;(
x,·) an Orlicz function of uniformly upper type 1 and lower type
p ∈ (0,1]. In this article, the authors introduce a new Musielak-Orlicz BMO-type space BMO
Aφ(
X) associated with the generalized approximation to the identity, give out its basic properties and establish its two equivalent characterizations, respectively, in terms of the spaces BMO
A, maxφ(
X) and
(
X). Moreover, two variants of the John-Nirenberg inequality on BMO
Aφ(
X) are obtained. As an application, the authors further prove that the space BMO
√Δφ(R
n),associated with the Poisson semigroup of the Laplace operator Δ on R
n, coincides with the space BMO
φ(R
n) introduced by Ky.