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Composition of rough singular integral operators on rearrangement invariant Banach type spaces
Authors
Jiawei Tan
Qingying Xue
Publication date
9 March 2024
Publisher
View
on
arXiv
Abstract
Let
Ξ©
\Omega
Ξ©
be a homogeneous function of degree zero and enjoy the vanishing condition on the unit sphere
S
n
β
1
(
n
β₯
2
)
\mathbb{S}^{n-1}(n\geq 2)
S
n
β
1
(
n
β₯
2
)
. Let
T
Ξ©
T_{\Omega}
T
Ξ©
β
be the convolution singular integral operator with kernel
Ξ©
(
x
)
β£
x
β£
β
n
{\Omega(x)}{|x|^{-n}}
Ξ©
(
x
)
β£
x
β£
β
n
. In this paper, when
Ξ©
β
L
β
(
S
n
β
1
)
\Omega \in L^{\infty}(\mathbb {S}^{n-1})
Ξ©
β
L
β
(
S
n
β
1
)
, we consider the quantitative weighted bounds of the composite operators of
T
Ξ©
T_{\Omega}
T
Ξ©
β
on rearrangement invariant Banach function spaces. These spaces contain the classical Lorentz spaces and Orlicz spaces as special examples. Weighted boundedness of the composite operators on rearrangement invariant quasi-Banach spaces were also given.Comment: 21 page
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Last time updated on 28/09/2024