与算子相关的Hardy空间上Riesz变换的端点估计
Endpoint Boundedness of Riesz Transforms onHardy Spaces Associated with Operators
设L1为L2(Rn)中一个满足Davies-Gaffney估计非负自伴算子,L2为一个具有复有界可测系数的二阶散度型椭圆算子。L1算子的一个典型例子即为薛定谔算子-Δ+V,其中Δ为Rn上的拉普拉斯算子而0≤V∈L1 loc(Rn). 对i∈{1,2}, 设H Li p(Rn)为相关于算子Li的Hardy空间。本文证明了在p=n/(n+1)的端点情形,Riesz变换D(L i -1/2)从H Li p(Rn)到经典的弱Hardy空间WH p(Rn)上有界。注意到,当p∈(n/(n+1),1]时,D(L i -1/2)从H Li p(Rn)到经典的Hardy空间H p(Rn)上有界。
Let L1 be a nonnegative self-adjointoperator in L2(Rn) satisfying the Davies-Gaffney estimates and L2 a second order divergence form elliptic operator with complexbounded measurable coefficients. A typical example of L1 is the Schrodinger operator -Δ+V, whereΔ is the Laplace operator on Rn and 0≤V∈L 1 loc(Rn). Let H p Li(Rn) be the Hardy space associated to Li for i∈{1,2}. In thispaper, the authors prove that the Riesz transform D (L i -1/2) is bounded from H p Li (Rn) to the classical weakHardy space WH p(Rn) in the critical case that p=n/(n+1).Recall that it is known that D (L i -1/2) is bounded from H p Li(Rn) to the classicalHardy space H p(Rn) when p∈(n/(n+1),1].
曹军、杨大春、杨四辈
数学
Riesz变换avies-Gaffney估计薛定谔算子二阶散度型椭圆算子Hardy空间弱Hardy空间原子分子极大函数
Riesz transformDavies-Gaffney estimateSchrodinger operatorsecond order elliptic operatorHardy spaceweak Hardy spaceatommoleculemaximal function
曹军,杨大春,杨四辈.与算子相关的Hardy空间上Riesz变换的端点估计[EB/OL].(2011-10-06)[2025-08-19].http://www.paper.edu.cn/releasepaper/content/201110-26.点此复制
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