Characterizations of BMO associated with Gauss measures via commutators of local fractional integrals |
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Authors: | Liguang Liu Dachun Yang |
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Institution: | 1.School of Mathematical Sciences,Beijing Normal University Laboratory of Mathematics and Complex Systems, Ministry of Education Beijing,Beijing,People’s Republic of China |
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Abstract: | Let dγ(x) ≡ π
−n/2
e
−|x|
2
dx for all x ∈ ℝ
n
be the Gauss measure on ℝ
n
. In this paper, the authors establish the characterizations of the space BMO(γ) of Mauceri and Meda via commutators of either local fractional integral operators or local fractional maximal operators.
To this end, the authors first prove that such a local fractional integral operator of order β is bounded from L
p
(γ) to L
p/(1−pβ)(γ), or from the Hardy space H
1(γ) of Mauceri and Meda to L
1/(1−β)(γ) or from L
1/β
(γ) to BMO(γ), where β ∈ (0, 1) and p ∈ (1, 1/β). |
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Keywords: | |
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