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	1. Entropy numbers of Besov classes of generalized smoothness onthe sphere
	WANG Heping,WANG Kai,WANG Jing
	Mathematics 11 January 2013
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	Abstract:Entropy numbers measure the compactness of operators(or the set) in a qualitative way. The asymptotic decay at infinityof the sequence of entropy numbers of a compact operator T describes the degree of compactness of T. They have manyapplication in the theory of function spaces and spectral theory, signal and image processing, probabilitytheory, learning theory,etc.. In this paper, the asymptoticbehavior of the entropy numbers of Besov classes$BB_{p, heta}^{Omega}(mathbb{S}^{d-1})$ of generalized smoothnesson the sphere in $L_q(ss)$ for $1leq p, q, hetaleqinfty$ isinvestigated, and their asymptotic orders are gotten. The exactorders of entropy numbers of Sobolev classes$BW_p^r(mathbb{S}^{d-1})$ in $L_q(mathbb{S}^{d-1})$ when $p$and/or $q$ is equal to $1$ or $infty$ are also obtained. Thisprovides the last piece as far as exact orders of entropy numbers of$BW_p^r(mathbb{S}^{d-1})$ in $L_q(mathbb{S}^{d-1})$ are concerned.
	TO cite this article:WANG Heping,WANG Kai,WANG Jing. Entropy numbers of Besov classes of generalized smoothness onthe sphere[OL].[11 January 2013] http://en.paper.edu.cn/en_releasepaper/content/4514334


	2. Uniqueness Theorem for p-adic Holomorphic Curves intersecting Hyperplanes without Counting Multiplicities
	Yan Qiming
	Mathematics 29 December 2012
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	Abstract:In this paper, a uniqueness theorem is proved for p-adic holomorphic curves into Pn(Cp) sharing 2n+2 hyperplanes located in general position withoutcounting multiplicities, which gives an improvement of Ru's result for 3n+1 hyperplanes located in general position .
	TO cite this article:Yan Qiming. Uniqueness Theorem for p-adic Holomorphic Curves intersecting Hyperplanes without Counting Multiplicities[OL].[29 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4502887

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	3. A Note on the Essential Norm of Composition Operators from $H^p(B_N)$ to $H^q(B_N)$
	Chen Zhihua,Jiang Liangying,Yan Qiming
	Mathematics 11 December 2012
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	Abstract:The authors give an upper bound of the essential normsof composition operators between Hardy spaces of the unit ball interms of the counting function in the higher dimensional valuedistribution theory defined by Professor S. S. Chern. The sufficientcondition for such operators to be bounded or compact is alsogiven.
	TO cite this article:Chen Zhihua,Jiang Liangying,Yan Qiming. A Note on the Essential Norm of Composition Operators from $H^p(B_N)$ to $H^q(B_N)$[OL].[11 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4502727


	4. Divergent Birkhoff normal forms of real analytic complex area preserving maps
	YIN Wanke
	Mathematics 07 December 2012
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	Abstract:In this paper, we provide a real analytic and complexvalued area preserving map, that possesses a divergent Birkhoffnormal form near an elliptic fixed point. The method uses the smalldivisor theory and the work of Gong in the study of the Halmitoniansystem.
	TO cite this article:YIN Wanke. Divergent Birkhoff normal forms of real analytic complex area preserving maps[OL].[ 7 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4501812


	5. On the Third Gap for Proper Holomorphic Maps between Balls
	HUANG Xiaojun,JI Shanyu,YIN Wanke
	Mathematics 07 December 2012
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	Abstract:In this paper, we study the gap rigidity phenomenon for proper holomorphic maps between balls of different dimension. We show that any F∈prop3(B n,B N), with 3n<N≤4n-7 and n≥7, is equivalent to a map of the form (G,0) with G∈Rat(B n,B 3n). The main ingredients for the proof of our main theorem are the normal form obtained by Huang-Ji-Xu and a lemma of the first author.
	TO cite this article:HUANG Xiaojun,JI Shanyu,YIN Wanke. On the Third Gap for Proper Holomorphic Maps between Balls[OL].[ 7 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4500337


	6. Birkhoff Interpolation of Cardinal Splines
	Ling Bo,Liu Yongping
	Mathematics 03 December 2012
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	Abstract:Cardinal SplineInterpolation Problem(CIP) is to consider finding a cardinal splinefunction s(x) of degree n such that s(v)= yv ,∀v∈Z, with given information (yv)v∈Z. Schoenberg solved this problem and the corresponding Cardinal Hermite Spline Interpolation Problem(CHIP) and obtained manygraceful results in about 1970. In this paper, the authors will considerCardinal (ρ0,ρ1,ρr-1) Birkhoff SplineInterpolation Problem(CBIP) using the similar method fromSchoenberg. For this purpose, the cardinal splines spaces S2m-1,∧1 with Birkhoff knots is introduced,where ∧1:={θ0,θ1,...,θr-1}∈ {0,...,2m-1} is an ordered set. The lacunary interpolation problemconsidered is to find the interpolation functions on Z with derivativesinformation of order ∧2:={ρ0,ρ1,...,ρr-1} in the spline space S2m-1,∧1. Here ∧2:={ρ0,ρ1,...,ρr-1}∈ {0,...,2m-1} is an ordered set.The necessary condition and several sufficient conditions on ∧1, ∧2 of the regularity(i.e. existing a uniquesolution) of CBIP are gained, and some results in CHIP areproved to be also true in CBIP.
	TO cite this article:Ling Bo,Liu Yongping. Birkhoff Interpolation of Cardinal Splines[OL].[ 3 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4499694


	7. Uncertainty inequalities for the Heisenberg group
	Xiao Jin-Sen , He Jian-Xun
	Mathematics 05 January 2012
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	Abstract:In this article, we extend the Heisenberg-Pauli-Weyl uncertainty inequality on the Euclidean space to the Heisenberg group. We use the estimate of the heat kernel together with the relation between thesublaplacian and the group Fourier transform to develop the uncertainty inequality on the Heisenberg group. By this inequality we obtain the Heisenberg-Pauli-Weyl uncertainty inequality for the continuous wavelet transform.
	TO cite this article:Xiao Jin-Sen , He Jian-Xun. Uncertainty inequalities for the Heisenberg group[OL].[ 5 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4459786


	8. Inverse Radon Transforms on the Heisenberg Group
	Zhong Xiao-Hong , He Jian-Xun
	Mathematics 31 December 2011
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	Abstract:In this article, we introduce a kind of unitary operator $U$associated with the involution on the Heisenberg group, invariant closed subspaces are identified with thecharacterization spaces of sub-Laplacian operators. In the senseof vector-valued functions, we study the theory of continuous wavelet transform. Also, we obtain a new inversion formula of Radon transform on the Heisenberg group $mathbf{H}^n$.
	TO cite this article:Zhong Xiao-Hong , He Jian-Xun. Inverse Radon Transforms on the Heisenberg Group[OL].[31 December 2011] http://en.paper.edu.cn/en_releasepaper/content/4458918


	9. Weighted Lp boundedness of Carleson type maximal operators
	DING Yong,LIU Honghai
	Mathematics 12 July 2011
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	Abstract:In 2001, Stein and Wainger have proved that Carleson type maximal operators is Lp bounded, where the phase function P(y) is polynomial without linear term and singular kernel K is smooth. In this artical, authors use TT* method to generalize Stein and Wainger's result, that is, Carleson type maximal operators is weighted Lp bounded for 1<p<∞, where phase function P(y) is polynomial without linear terms, K(y)=Ω(y)/\|y\|n, Ω satisfies Lq-Dini condition, 1<q≤∞.
	TO cite this article:DING Yong,LIU Honghai. Weighted Lp boundedness of Carleson type maximal operators[OL].[12 July 2011] http://en.paper.edu.cn/en_releasepaper/content/4435360


	10. Lp boundedness of Carleson type maximal operators with nonsmooth kernels
	DING Yong,LIU Honghai
	Mathematics 12 July 2011
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	Abstract:Stein and Wainger have proved that Carleson type maximal operators is Lp bounded, where the phase function P(y) is polynomial without linear term and singular kernel K is smooth. In this artical, authors consider another kind of Carleson type maximal operators, where the phase function is P(\|y\|), P(t) is a polynomial on R without linear term, K(y)=Ω(y)/\|y\|n, Ω∈H1(Sn-1). They obtain the Lp boundedness for this kind of Carleson type maximal operators by Stein-Wainger's TT* argument and Calderon-Zygmund's rotation method.
	TO cite this article:DING Yong,LIU Honghai. Lp boundedness of Carleson type maximal operators with nonsmooth kernels[OL].[12 July 2011] http://en.paper.edu.cn/en_releasepaper/content/4435357

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