Commutators of Calderón-Zygmund operators related to admissible functions on spaces of homogeneous type and applications to Schrödinger operators
Tóm tắt
Let X be an RD-space. In this paper, the authors establish the boundedness of the commutator T
b
f = bT f − T(bf) on L
p
, p ∈ (1,∞), where T is a Calderón-Zygmund operator related to the admissible function ρ and b ∈ BMO
θ
(X) ⊇ BMO(X). Moreover, they prove that T
b
is bounded from the Hardy space H
1
(X) into the weak Lebesgue space L
weak
1
(X). This can be used to deal with the Schrödinger operators and Schrödinger type operators on the Euclidean space ℝ
n
and the sub-Laplace Schrödinger operators on the stratified Lie group
$\mathbb{G}$
.
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