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为您找到包含“The first author is supported by NationalNatural Science Foundation”的内容共2

CAO Jun,Yang Dachun,YANG Sibei

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].

2011-10-06

The first author is supported by NationalNatural Science Foundation (Grant No. 11171027

School of Mathematical Sciences,Beijing Normal University, Laboratory of Mathematics and Complex Systems,Ministry of Education,School of Mathematical Sciences,Beijing Normal University, Laboratory of Mathematics and Complex Systems,Ministry of Education,School of Mathematical Sciences,Beijing Normal University, Laboratory of Mathematics and Complex Systems,Ministry of Education

#Mathematics#

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Lu Guangcun,Chen Xiaomin

In this article, for a compact special Legendrian submanifold withboundary of contact Calabi-Yau manifolds we study the deformationof it with boundary confined in an appropriately chosen contactsubmanifold of codimension two which we also call a scafford(Definition 4) by analogy with Butsher[1].Our result shows that it cannot bedeformed under such a boundary confinement. This result may be viewedas supplements of the compact boundless case considered by Tomassini andVezzoni[2].

2011-12-12

Research Fund for theDoctoral Program Higher Education of China (200800270003

The first author is supported by NationalNatural Science Foundation (Grant No. 10971014

School of Mathematical Sciences, Beijing Normal University, Beijing 100875,Department of Mathematics, China University of Petroleum, Beijing 102249

#Mathematics#

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