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	1. A restriction theorem for the quaternion Heisenberg group
	Liu Heping,Wang Yingzhan
	Mathematics 28 January 2011
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	Abstract:We prove that the restriction operator for the sublaplacian on the quaternion Heisenberg group is bounded from Lp to Lp' if 1<=p=<3/4 . This is different from the Heisenberg group, on which the restriction operator is not bounded from Lp to Lp' unless p=1.
	TO cite this article:Liu Heping,Wang Yingzhan. A restriction theorem for the quaternion Heisenberg group[OL].[28 January 2011] http://en.paper.edu.cn/en_releasepaper/content/4409526


	2. Boundedness of Operators in Generalized Morrey Spaces on Homogeneous Spaces
	Weijie Hou
	Mathematics 07 September 2009
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	Abstract:Maximal operators play a very important role in harmonic analysis and have many important applications. The classical Morrey spaces were introduced by Morrey to study the local behaviour of solutions to second order elliptic partial differential equations . Since then, these spaces play an important role in studying the regularity of solutions to partical differential equations. As Morrey spaces may be considered as an extension of Lebesgue spaces, it is natrural and important to study the boundedness for operators in Morrey spaces.Much work has been done.In this pape, the author establish the boundeness of generalized maximal operators in Morrey spaces on homogeneous spaces and obtain some equivaleut conditions about theboundeness of generalized maximal operators.This paper extended the known results.
	TO cite this article:Weijie Hou. Boundedness of Operators in Generalized Morrey Spaces on Homogeneous Spaces[OL].[ 7 September 2009] http://en.paper.edu.cn/en_releasepaper/content/34960

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	3. Endpoint Estimate for Commutator of Riesz Transform Associated with
	Pengtao Li,Lizhong Peng
	Mathematics 22 July 2009
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	Abstract:In this paper, we will discuss the H1L boundedness of commutator of Riesz transform associated with Schrödinger operator L = −Δ + V, where H1L (Rn) be the Hardy space associated with L. We assume that V (x) is a nonzero, nonnegative potential and belongs to Bq for some q > n/2. Let T1 = V (x)(− Δ+V )−1 , T2 = V 1/2(−Δ+V )−1/2 and T3 = ▽(−Δ+V )−1/2 , we obtain that, for b ∈ BMO(Rn), the commutator [b, Ti], (i =1, 2, 3) are of (H1L ,L1weak ) boundedness.
	TO cite this article:Pengtao Li,Lizhong Peng. Endpoint Estimate for Commutator of Riesz Transform Associated with[OL].[22 July 2009] http://en.paper.edu.cn/en_releasepaper/content/34003


	4. Inversion Formulas for the Spherical Radon-Dunkl Transform
	Zhongkai Li,Song Futao
	Mathematics 14 January 2009
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	Abstract:The spherical Radon-Dunkl transform R_{kappa}, associated to weight functions invariant under a finite reflection group, is introduced,and some elementary properties are obtained in terms of $h$-harmonics. Several inversion formulas of $R_{kappa}$ are given with the aid of spherical Riesz-Dunkl potentials, the Dunkl operators, and some appropriate wavelet transforms.
	TO cite this article:Zhongkai Li,Song Futao. Inversion Formulas for the Spherical Radon-Dunkl Transform[OL].[14 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27760


	5. A Generalized Radon Transform on the Plane
	Zhongkai Li,Song Futao
	Mathematics 12 January 2009
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	Abstract:A new generalized Radon transform $R_{alpha,,beta}$ on the plane for functions even in each variable is defined, which has natural connections with the bivariate Hankel transform, the generalized biaxially symmetric potential operator $Delta_{alpha,,beta}$ and the Jacobi polynomials $P_k^{(beta,,alpha)}(t)$. The transform $R_{alpha,,beta}$ and its dual $R_{alpha,,beta}^ast$ are studied in a systematic way, and in particular, the generalized Fuglede formula and some inversion formulas for $R_{alpha,,beta}$ for functions in $L_{alpha,,beta}^p(RR^2_+)$ are obtained in terms of the bivariate Hankel-Riesz potential. Moreover, the transform $R_{alpha,,beta}$ is used to represent the solutions of the partial differential equations $Lu:=sum_{j=1}^m a_jDelta_{alpha,,beta}^ju=f$ with constant coefficients $a_j$\
	TO cite this article:Zhongkai Li,Song Futao. A Generalized Radon Transform on the Plane[OL].[12 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27671


	6. Weighted Boundedness of Sublinear Operators in Morrey Spaces.
	Hou Weijie,Liu Mingju
	Mathematics 04 December 2008
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	Abstract:The classical Morrey spaces were introduced by Morrey to study the local behaviour of solutions to second order elliptic partial differential equations. Since then these spaces play a very import role in studying the regularity of solutions to second order elliptic partial differential equations.As Morrey spaces may be considered as an extension of Lebesgue spaces, it is natural and important to study the weighted boundedness for operaters in Morrey spaces. Much work in this direction has been done.The studying of sublinear operators is very active these years, in this paper, the authors introduce a type of topological structure in the Cartesian product and a set function, and in advance discuss weighted boundedness of sublinear operators in Morrey spaces. The result improve and extend the known results.
	TO cite this article:Hou Weijie,Liu Mingju. Weighted Boundedness of Sublinear Operators in Morrey Spaces.[OL].[ 4 December 2008] http://en.paper.edu.cn/en_releasepaper/content/26315


	7. Boundeness of Generalized Maximal Operaters on Homogeneous Spaces
	Weijie Hou , Liu Mingju
	Mathematics 25 November 2008
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	Abstract: Maximal functions play a very important role in harmonic analysis. The classical Morrey spaces were introduced by Morrey to study the local behaviour of solutions to second order elliptic partial differential equations. Since then, these spaces play an important role in studying the regularity of solutions to partial differential equations. As homogeneous spaces may be considered as an extension of R^n spaces, it is natural and important to study the boundeness for operaters in Morrey spaces on homogeneous spaces. In this paper, the authors introduce a type of topological structure in the Cartesian product and a set function mapping the balls on homogeneous spaces into the sets in the Cartesian product , and obtain boundeness of generalized operators in Morrey spaces 。Some results have been obtained and the result in this paper improve and extend the known results.
	TO cite this article:Weijie Hou , Liu Mingju . Boundeness of Generalized Maximal Operaters on Homogeneous Spaces[OL].[25 November 2008] http://en.paper.edu.cn/en_releasepaper/content/26015


	8. A Parabolic Singular Integral Operator With Rough Kernel
	Yanping Chen,Yong Ding,Dashan Fan
	Mathematics 25 September 2008
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	Abstract:Let $Omega$ be an $H^1(S^{n-1})$ function on the unit sphere satisfying a certain cancellation condition. We study the $L^p$ boundedness of the singular integral operator $$T f(x)=hbox{p.v.}int_{{\\Bbb R}^n}f(x-y)Omega(y^prime)rho(y)^{-alpha},dy,$$ where $alphageq n$ and $rho$ is a norm function which is homogeneous with respect to certain nonistropic dilation. The result in the paper substantially improves and extends some known results.
	TO cite this article:Yanping Chen,Yong Ding,Dashan Fan. A Parabolic Singular Integral Operator With Rough Kernel[OL].[25 September 2008] http://en.paper.edu.cn/en_releasepaper/content/24364


	9. The Decomposition of Product Space $H^{1}_{L}\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\times BMO_{L}$
	Li Pengtao ,Peng Lizhong
	Mathematics 27 May 2008
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	Abstract:In analogy with classical results([BIJZ]), we prove that functions in the product of the Hardy space $H^{1}_{L}$ associated with Schr“{o}dinger operators $L=-triangle+V$ and its dual space $BMO_{L}$ admit a suitable decomposition. We obtain that for $fin H^{1}_{L}$ and $bin BMO_{L}$, the point-wise product $b cdot f$ as a Schwartz distribution, denoted by $b times f in S＇(R^{n})$, can be decomposed in two parts; precisely, $b times f=u+v$ where $u in L^{1}(R^{n})$ while $v$ lies in Hardy-Orlicz space associated with Schr”{o}dinger operators $H^{{mathcal{P}}}_{L}(R^{n},d mu)$.
	TO cite this article:Li Pengtao ,Peng Lizhong . The Decomposition of Product Space $H^{1}_{L}\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\times BMO_{L}$[OL].[27 May 2008] http://en.paper.edu.cn/en_releasepaper/content/21797


	10. Compactness of Commutator of Riesz transforms Associated to Schroginger operator
	Pengtao Li,Lizhong Peng
	Mathematics 06 May 2008
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	Abstract:In this paper, we consider the compactness of some commutators of Riesz transforms associated to Schr\\\"{o}dinger operator $L=-triangle+V(x)$ on $R^{n}, ngeq 3.$ We assume that $V(x)$ is non-zero, nonnegative and belongs to the reverse H\\\"{o}lder class $B_{q}$ for $q>frac{n}{2}$. Let $T_{1}=(-triangle+V)^{-1}V,quad T_{2}=(-triangle+V)^{-1/2}V^{1/2}$ and $T_{3}=(-triangle+V)^{-1/2}nabla$, we obtain the commutator operators $[b,T_{j}], (j=1,2,3)$ are compact operators on $L^{p}(R^{n})$ when $p$ ranges in an interval, where $bin VMO(R^{n})$.
	TO cite this article:Pengtao Li,Lizhong Peng. Compactness of Commutator of Riesz transforms Associated to Schroginger operator[OL].[ 6 May 2008] http://en.paper.edu.cn/en_releasepaper/content/21165

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