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	1. The boundedness of higher order Riesz transform associated with Sch
	SHEN Jian-Chun,Dong Jianfeng
	Mathematics 04 January 2015
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	Abstract:Let $L=-Delta+V$ be a Schr"{o}dinger operator on $mathbb{R}^n$ ($n geq 3$) , where $V ot equiv 0$ is a nonnegative potential belonging to certain reverse H"{o}lder class $B_s$ for $s geq n$. The Hardy type spaces $H_L^p, rac{n}{n+delta}<pleq 1$ for some $delta >0$, are defined in terms of the maximal function with respect to the semigroup ${e^{-tL} }_{t>0}$. In this article, we investigate the boundedness of some integral operator related to $L$, such as $VL^{-1}$, $Delta L^{-1}$ and $ abla^2 L^{-1}$, on spaces $H_L^p(mathbb{R}^n)$.
	TO cite this article:SHEN Jian-Chun,Dong Jianfeng. The boundedness of higher order Riesz transform associated with Sch[OL].[ 4 January 2015] http://en.paper.edu.cn/en_releasepaper/content/4626619


	2. Dyadic sets, maximal functions and applications on$ax+b$,-groups
	LIU Li-Guang,Maria Vallarino,YANG Da-Chun
	Mathematics 19 March 2011
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	Abstract:Let $S$ be the Lie group${mathbb R}^nltimes {mathbb R}$, where ${mathbb R}$acts on ${mathbb R}^n$ by dilations,endowed with the left-invariantRiemannian symmetric space structure and the right Haar measure$ ho$, which is a Lie group of exponential growth. Hebisch andSteger in [Math. Z. 245(2003), 37-61] proved that any integrablefunction on $(S, ho)$ admits a Calder'on-Zygmund decompositionwhich involves a particular family of sets, calledCalder'on-Zygmund sets. In this paper, we show theexistence of a dyadic grid in the group $S$, which has {nice} propertiessimilar to the classical Euclidean dyadic cubes. Using theproperties of the dyadic grid, we prove aFefferman-Stein type inequality, involving the dyadic Hardy-Littlewoodmaximal function and the dyadic sharp function. As a consequence,we obtain a complex interpolationtheorem involving the Hardy space $H^1$ and the space${mathopmathrm{,BMO,}}$introduced in [Collect. Math. 60(2009), 277-295].
	TO cite this article:LIU Li-Guang,Maria Vallarino,YANG Da-Chun. Dyadic sets, maximal functions and applications on$ax+b$,-groups[OL].[19 March 2011] http://en.paper.edu.cn/en_releasepaper/content/4417246

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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. Entire solutions of a certain type of functional-differential equation
	Xiao-Bin Zhang,Hong-Xun Yi
	Mathematics 25 June 2009
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	Abstract:In this paper, we shall utilize Nevanlinna value distribution theory and normal family to study the solvability of a certain type of functional-differential equation of the form f(z1+z2) = f(z1)f\
	TO cite this article:Xiao-Bin Zhang,Hong-Xun Yi. Entire solutions of a certain type of functional-differential equation[OL].[25 June 2009] http://en.paper.edu.cn/en_releasepaper/content/33407


	5. DISTORTION THEOREMS FOR BLOCH MAPPINGS ON THE UNIT POLYDISC ${D}^n
	wangjianfei ,Liu Taishun,Tang Xiaomin
	Mathematics 13 January 2009
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	Abstract:In this paper, we establish distortion theorems for some various subfamilies of Bloch mappings defined in the unit polydisc $D^n$ with critical points, which extend the results of Liu and Minda to higher dimensions. We obtain lower bounds on $\|\\\\det (f\\\
	TO cite this article: wangjianfei ,Liu Taishun,Tang Xiaomin. DISTORTION THEOREMS FOR BLOCH MAPPINGS ON THE UNIT POLYDISC ${D}^n[OL].[13 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27735


	6. Distortion theorems on the Lie ball RIV(n) in Cn
	wangjianfei,Liu Taishun,Xu Huiming
	Mathematics 12 January 2009
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	Abstract:In this paper, we introduce the subfamilies Hm(RIV(n)) of holomorphic mappings defined on the Lie ball RIV(n) which take into consideration the m-order to which the Jacobian determinant must vanish, as well as for the limiting case of locally biholomorphic mappings. Various distortion theorems for holomophic mappings Hm(RIV(n)) are established. The distortion theorems coincide with Liu and Minda as the special case of the unit disk. When m = 1 and m ! +1, the distortion theoerems reduce to the results obtained by Gong for RIV(n), respectively. Moreover, our method is different. As an application, the bounds for Bloch constants of Hm(RIV(n)) are given.
	TO cite this article:wangjianfei,Liu Taishun,Xu Huiming. Distortion theorems on the Lie ball RIV(n) in Cn[OL].[12 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27691


	7. 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


	8. A Way of Constructing Approximate Interpolating Neural Networks
	ding lei,sheng baohuai
	Mathematics 05 December 2008
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	Abstract:In this paper, we present a type of single-hidden layer feedforward neural networks with thin-plate spline activation function. We find they can approximately interpolate, with arbitrary precision, any set of distinct data in one dimensions or multidimensional. They can uniformly approximate the continuous function of one variable as well as several variables.
	TO cite this article:ding lei,sheng baohuai. A Way of Constructing Approximate Interpolating Neural Networks[OL].[ 5 December 2008] http://en.paper.edu.cn/en_releasepaper/content/26338


	9. 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


	10. On the solution of Dirichlet’s problem of complex Monge-Amp`ere equation on Cartan-Hartogs domain of the second type
	Yin Weiping,Yin Xiaolan
	Mathematics 26 May 2008
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	Abstract:Complex Monge-Amp`ere equation is a nonlinear equation with high degree, therefore to get its solution is very difficult. In present paper how to get the solution of Dirichlet’s problem of Complex Monge-Amp`ere equation on the Cartan-Hartogs domain of the second type is discussed by using the analytic method. Firstly, the complex Monge-Amp`ere equation is reduced to the nonlinear ordinary differential equation, then the solution of the Dirichlet’s problem of complex Monge-Amp`ere equation is reduced to the solution of two point boundary value problem of the nonlinear second-order ordinary differential equation. Secondly, the solution of the Dirichlet’s problem is given in semiexplicit formula, and under the special case the exact solution is obtained. These results may be helpful for the numerical method of Dirichlet’s problem of complex Monge-Amp`ere equation on the Cartan-Hartogs domain.
	TO cite this article:Yin Weiping,Yin Xiaolan. On the solution of Dirichlet’s problem of complex Monge-Amp`ere equation on Cartan-Hartogs domain of the second type[OL].[26 May 2008] http://en.paper.edu.cn/en_releasepaper/content/21774

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