新疆大学数学与系统科学学院
纸质出版:2017
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[1]张惠,齐春燕,李宝德.各向异性分数次积分算子的加权估计(英文)[J].新疆大学学报(自然科学版),2017,34(01):35-39.
[1]张惠,齐春燕,李宝德.各向异性分数次积分算子的加权估计(英文)[J].新疆大学学报(自然科学版),2017,34(01):35-39. DOI: 10.13568/j.cnki.651094.2017.01.007.
DOI:10.13568/j.cnki.651094.2017.01.007.
设A是一个扩张矩阵
α∈[0
1)
p∈(1
1/α)且q:=(1/p-α)-1
如果非负函数v满足各向异性的Muckenhoupt Ap
q(A)权条件
那么各向异性的分数次极大函数f*α从Lp(Rn
vp)到Lq(Rn
vq)是有界的.作为应用
作者进一步证明了v∈Ap
q(A)当且仅当各向异性分数次积分算子Tα
A从Lp(Rn
vp)到Lq(Rn
vq)是有界的
这些结论是Muckenhoupt和Wheeden的结果在各向异性情形下的推广(Trans Amer Math Soc
192:261-274
1974).
Let A be an expansive dilation
α ∈ [0
1)
p ∈(1
1/α) and q :=(1/p-α)-1. The authors prove that:if the nonnegative function v satisfies the anisotropic Muckenhoupt condition Ap
q(A)
then the anisotropic fractional maximal function f*αis bounded from Lp(Rn
vp) to Lq(Rn
vq). As an application
the authors further obtain that v ∈ Ap
q(A) if and only if the anisotropic fractional integral operator Tpα
Ais bounded from L(Rn
vp) to Lq(Rn
vq)
which are anisotropic variants of Muckenhoupt and Wheeden(Trans Amer Math Soc
192:261-274
1974).
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