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	1. 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


	2. An Off-Diagonal Marcinkiewicz Interpolation Theorem on Lorentz Spaces
	, LIU Li-Guangffil{2} and YANG Da-Chun,
	Mathematics 09 March 2011
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	Abstract:Let (X,u) be a measure space. In thispaper, using some ideas from L. Grafakos and N. Kalton, the authorsestablish an off-diagonal Marcinkiewicz interpolation theorem for aquasilinear operator T in Lorentz spaces Lp,q(X) with p,q∈(0,∞], which is a corrected version of Theorem1.4.19 in [L. Grafakos, Classical Fourier Analysis, Second Edition,Graduate Texts in Math., No. 249, Springer, New York, 2008] andwhich, in the case that T is linear or nonnegative sublinear, p∈[1,∞)and q∈[1,∞), was obtained by E. M. Steinand G. Weiss [Introduction to Fourier Analysis on Euclidean spaces,Princeton University Press, Princeton,N.J., 1971].
	TO cite this article:, LIU Li-Guangffil{2} and YANG Da-Chun,. An Off-Diagonal Marcinkiewicz Interpolation Theorem on Lorentz Spaces[OL].[ 9 March 2011] http://en.paper.edu.cn/en_releasepaper/content/4413031

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	3. 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


	4. Small Support Spline Riesz Wavelets in Low Dimensions
	HAN Bin,MO Qun,SHEN Zuowei
	Mathematics 26 January 2011
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	Abstract:B.~Han and Z.~Shen constructed afamily of univariate short support Riesz waveletsfrom uniform B-splines in 2006. A bivariate spline Riesz wavelet basis fromthe Loop scheme was derived by B.~Han and Z.~Shen in 2005.Motivated bythese two papers, we develop in this article ageneral theory and a construction method to derive small supportRiesz wavelets in low dimensions from refinable functions. Inparticular, we obtain small support spline Riesz wavelets frombivariate and trivariate box splines. Small support Riesz waveletsare desirable for developing efficient algorithms in variousapplications. For example, the short support Riesz wavelets constructed byB.~Han and Z.~Shen were used in a surface fitting algorithm byM.J.~Johnson, Z.~Shen and Y.H.~Xu in 2009, and the Riesz wavelet basis from the Loop scheme wasused in a very efficient geometric mesh compression algorithm byA. Khodakovsky, P. Schr"oder and W. Sweldens in 2000.
	TO cite this article:HAN Bin,MO Qun,SHEN Zuowei. Small Support Spline Riesz Wavelets in Low Dimensions[OL].[26 January 2011] http://en.paper.edu.cn/en_releasepaper/content/4408648


	5. Remark on the Restricted Isometry Property in Orthogonal Matching Pursuit
	MO Qun,SHEN Yi
	Mathematics 26 January 2011
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	Abstract:This paper demonstrates theoretically that if the restrictedisometry constant of the compressed sensing matrixsatisfies a sufficient condition,then a greedy algorithm called Orthogonal Matching Pursuit (OMP) canrecover a signal with K nonzero entries in K iterations. Incontrast, matrices are also constructed with restricted isometryconstant satisfying a stronger conditionsuch that OMP can not recover K-sparse x in K iterations. Thisresult shows that the conjecture given by Dai and Milenkovic is true.
	TO cite this article:MO Qun,SHEN Yi. Remark on the Restricted Isometry Property in Orthogonal Matching Pursuit[OL].[26 January 2011] http://en.paper.edu.cn/en_releasepaper/content/4408549


	6. ON BOUNDARY BEHAVIOR OF THE CAUCHY TYPE INTEGRAL IN HYPERCOMPLEX ANALYSIS
	Du Jinyuan
	Mathematics 04 May 2010
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	Abstract:We survey the researches of the boundary behavior for the Cauchy type integrals defined on a smooth closed surface in the Euclidean space with values on the Clifford algebra, or defined on the distinguished boundary of the direct product of two domains with values on the universal Clifford algebra, which includes Sochocki-Plemelj formulae and Privalov-Muskhelishvili theorems, Poincare-Bertrand formulae. Then some boundary value problems and singular integral equation in Clifford analysis are introduced.
	TO cite this article:Du Jinyuan. ON BOUNDARY BEHAVIOR OF THE CAUCHY TYPE INTEGRAL IN HYPERCOMPLEX ANALYSIS[OL].[ 4 May 2010] http://en.paper.edu.cn/en_releasepaper/content/42553


	7. Wavelet characterization for multipliers on Sobolev spaces
	Yang Qixiang
	Mathematics 02 April 2010
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	Abstract:Multipliers on Sobolev spaces have been studied heavily in 1980s and stay always as an active topic. Before, one used the capacity of compact set on Sobolev spaces to characterize multiplier spaces and to study the applications related to multiplier spaces, one did not know even they have unconditional basis or not. Here wavelet methods are introduced, the structure of multiplier spaces is analyzed through the following conceptions: some special decomposition of product of functions, Morrey spaces, known wavelet characterization of certain function spaces, dual and the relations between function spaces; and the conclusion of the elements of multiplier spaces are determined by the absolute value of their wavelet coefficient is drawed.
	TO cite this article:Yang Qixiang. Wavelet characterization for multipliers on Sobolev spaces[OL].[ 2 April 2010] http://en.paper.edu.cn/en_releasepaper/content/41508


	8. Uniqueness of entire functions and differential polynomials sharing one value
	Zhang Xiaobin ,Meng Dawei
	Mathematics 29 October 2009
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	Abstract:In this paper, we shall utilize Nevanlinna value distribution theory to study the uniqueness problems on entire functions and differential polynomials sharing one value. Our theorems improve or generalize some results of Zhang and Lin, Chen, Zhang, Lin and Chen and so on.
	TO cite this article:Zhang Xiaobin ,Meng Dawei . Uniqueness of entire functions and differential polynomials sharing one value[OL].[29 October 2009] http://en.paper.edu.cn/en_releasepaper/content/36230


	9. Further results about the normal family of meromorphic functions and shared sets
	Qi Jianming
	Mathematics 18 September 2009
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	Abstract:Let $\\mathcal{F}$ be a family of meromorphic functions in a domain $D$, and let $k$, $n(\\geq 2)$ be two positive integers, and let $S=\\{a_1, a_2,..., a_n\\}$, where $a_1, a_2,..., a_n$ are distinct finite complex numbers. If for each $f\\in\\mathcal{F}$, all zeros of $f$ have multiplicity at least $k+1$, and $f$ and $G(f)$ share the set $S$ in $D$, where $G(f)=P(f^{(k)})+H(f)$ is a differential polynomial of $f$, then $\\mathcal{F}$ is normal in $D$.
	TO cite this article:Qi Jianming . Further results about the normal family of meromorphic functions and shared sets[OL].[18 September 2009] http://en.paper.edu.cn/en_releasepaper/content/35294


	10. 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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