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Endpoint Boundedness of Riesz Transforms onHardy Spaces Associated with Operators
CAO Jun,Yang Dachun *,YANG Sibei
School of Mathematical Sciences,Beijing Normal University, Laboratory of Mathematics and Complex Systems,Ministry of Education
*Correspondence author
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Funding: The first author is supported by NationalNatural Science Foundation （No.Grant No. 11171027）
Opened online: 6 October 2011
Accepted by: none
Citation: CAO Jun,Yang Dachun,YANG Sibei.Endpoint Boundedness of Riesz Transforms onHardy Spaces Associated with Operators[OL]. [ 6 October 2011] http://en.paper.edu.cn/en_releasepaper/content/4444453
 
 
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].
Keywords:Riesz transform; Davies-Gaffney estimate; Schrodinger operator; second order elliptic operator; Hardy space; weak Hardy space; atom; molecule; maximal function
 
 
 

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