Author:
Bui The Anh,Duong Xuan Thinh
Abstract
AbstractLet $$(X, d, \mu )$$
(
X
,
d
,
μ
)
be a space of homogeneous type. Let L be a nonnegative self-adjoint operator on $$L^2(X)$$
L
2
(
X
)
satisfying certain conditions on the heat kernel estimates which are motivated from the heat kernel of the Schrödinger operator on $$\mathbb {R}^n$$
R
n
. The main aim of this paper is to prove a new atomic decomposition for the Besov space $$\dot{B}^{0, L}_{1,1}(X)$$
B
˙
1
,
1
0
,
L
(
X
)
associated with the operator L. As a consequence, we prove the boundedness of the Riesz transform associated with L on the Besov space $$\dot{B}^{0, L}_{1,1}(X)$$
B
˙
1
,
1
0
,
L
(
X
)
.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Mathematics,Analysis
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