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	1. ON BOUNDARY PROBLEMS FOR BEGULAR FUNCTIONS IN HYPERCOMPLEX ANALYSIS
	Jinyuan DU,Pei DANG
	Mathematics 18 February 2014
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	Abstract:In this article, the authors survey and review the recent studies of boundary value problems for regular functions in Clifford analysis, which include theoretical foundations and useful methods. These theoretical bases consist of the generalized Cauchy theorem and the generalized Cauchy integral formula, the Painlev'{e} type theorem and the boundary behaviors of the Cauchy type integrals, as well as various integral representations. Certain boundary value problems and singular integral equations in the Clifford algebra setting are introduced.
	TO cite this article:Jinyuan DU,Pei DANG. ON BOUNDARY PROBLEMS FOR BEGULAR FUNCTIONS IN HYPERCOMPLEX ANALYSIS[OL].[18 February 2014] http://en.paper.edu.cn/en_releasepaper/content/4585849


	2. Strichartz estimates for the wave equation with full Laplacian on the quaternion Heisenberg group
	SONG Naiqi,ZHAO Jiman
	Mathematics 16 January 2014
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	Abstract:In this article, we prove dispersive and Strichartz estimates for the solution of the wave equationrelated to the full Laplacian on the quaternion Heisenberg group, by means of homogeneous Besov spacedefined by a Littlewood-Paley decomposition related to the full Laplacian.
	TO cite this article:SONG Naiqi,ZHAO Jiman. Strichartz estimates for the wave equation with full Laplacian on the quaternion Heisenberg group[OL].[16 January 2014] http://en.paper.edu.cn/en_releasepaper/content/4581622

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	3. On the escaping set of meromorphic functions with direct tracts
	Xuan Zu-Xing, Zheng Jian-Hua
	Mathematics 23 December 2013
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	Abstract: Suppose that $f$ is a transcendental meromorphic function with at least one direct tract. In this note, we investigate the structure of the escaping set. We also give a theorem which is about the slowing escaping set.
	TO cite this article:Xuan Zu-Xing, Zheng Jian-Hua. On the escaping set of meromorphic functions with direct tracts[OL].[23 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4577829


	4. Geometry and ergodic theory of parabolic meromorphic functions
	Xuan Zu-Xing,Zheng Jian-Hua
	Mathematics 20 December 2013
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	Abstract:Let $f$ be a parabolic transcendental meromorphic function with positive and finite order $ ho$ and its derivative satisfies some growth conditions. In this paper, we show the existence of conformal measures and use this basic tool to illustrate both geometrical and dynamical features of the radial Julia set. We also characterize the conformal measures supported on radial Julia sets.
	TO cite this article:Xuan Zu-Xing,Zheng Jian-Hua. Geometry and ergodic theory of parabolic meromorphic functions[OL].[20 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4576334


	5. On quasiconformal mappings which keepthe boundary points fixed
	Hu Yun,Shen Yuliang
	Mathematics 21 November 2013
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	Abstract:In 1960's Kra asked whether $tmu$ $(0<t<1)$ is a trivial Beltrami coefficient whenever $mu$ is trivial, and Gehring and Reich-Strebel independently gave some counter-examples to this question. In this short note we will discuss Kra's question in another direction, namely, we are concerned with those Beltrami coefficients $mu$ such that all $tmu$ $(0le tle 1)$ are trivial. An application is given to the geodesic segments in infinite dimensional Teichm"uller spaces.
	TO cite this article:Hu Yun,Shen Yuliang. On quasiconformal mappings which keepthe boundary points fixed[OL].[21 November 2013] http://en.paper.edu.cn/en_releasepaper/content/4571179


	6. Hajl asz gradients are upper gradients
	JIANG RENJIN, NAGESWARI SHANMUGALINGAM,YANG DACHUN, YUAN WEN
	Mathematics 10 November 2013
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	Abstract:Let $(X, d, mu)$ be a metric measure space, with $mu$ a Borel regular measure.In this paper, we prove that, if $uin L^1_loc(X)$ and $g$ is aHajl asz gradient of $u$, then there exists $widetilde u$ such that$widetilde u=u$almost everywhere and $4g$ is a $p$-weakupper gradient of $widetilde u$. This result avoids a priori assumptionon the quasi-continuity of $u$ used in [Rev. Mat. Iberoamericana 16 (2000), 243-279].As an application, an embedding of the Morrey-type function spaces based on Hajl asz-gradientsinto the corresponding function spaces based on upper gradients is obtained. We also introducethe notion of local Hajl asz gradient, and investigate the relations between local Hajl asz gradientand upper gradient.
	TO cite this article:JIANG RENJIN, NAGESWARI SHANMUGALINGAM,YANG DACHUN, et al. Hajl asz gradients are upper gradients[OL].[10 November 2013] http://en.paper.edu.cn/en_releasepaper/content/4568999


	7. A note on geodesic segments in infinite dimensional Teichmuller spaces
	Hu Yun,Shen Yuliang
	Mathematics 27 October 2013
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	Abstract:It is proved that in any infinite dimensional Teichm"uller space, if there exist more than one geodesic segments between two points, then there must exist infinitely many geodesic segments joining them such that each pair of these geodesic segments are tangent to each other at both endpoints. This answers a question posed by Z. Li in 2012.
	TO cite this article:Hu Yun,Shen Yuliang. A note on geodesic segments in infinite dimensional Teichmuller spaces[OL].[27 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4566223


	8. Strong summation of Cesaro means of Fourier-Laplace series
	Zhang Wei,Zhang Xi-Rong
	Mathematics 10 October 2013
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	Abstract:The strong summation of Fourier-Laplace series in logarithmic subclasses of $L^{2}(sum_{d})$ defined in terms of moduli of continuity is of interest.In this note,the almost everywhere convergence rates of the Cesaro means for Fourier-Laplace series of the convex subclasses areobtained.The strong approximation order of the Cesaro means and the partial summation operators are also presented.
	TO cite this article:Zhang Wei,Zhang Xi-Rong. Strong summation of Cesaro means of Fourier-Laplace series[OL].[10 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4563503


	9. Interpolation of Morrey Spaces on MetricMeasure Spaces
	Lu Yufeng,Yang Dachun,Yuan Wen
	Mathematics 20 February 2013
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	Abstract:In this article, via the classical complex interpolation methodand some interpolation methods traced to Gagliardo,the authors obtain an interpolation theorem forMorrey spaces on quasi-metric measure spaces, which generalizessome known results on Rn.
	TO cite this article:Lu Yufeng,Yang Dachun,Yuan Wen. Interpolation of Morrey Spaces on MetricMeasure Spaces[OL].[20 February 2013] http://en.paper.edu.cn/en_releasepaper/content/4521984


	10. Optimal recovery of functions on the sphere on a Sobolev spaces with a Gaussian measure in the average case setting
	HUANG Zexia,WANG He-Ping
	Mathematics 11 January 2013
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	Abstract:Optimal recovery means that using finitely manyarbitrary function values f(x) for some x∈D to reconstruct(recovery) functions f from a given classes with the least possible errors. Optimal recovery constitutes a important ingredient innumerical analysis and has many important practical applications.There are two most important case setting: worst case setting andaverage case setting as far as error measure is concerned. In thispaper, optimal recovery (reconstruction) of functions on the spherein the average case setting is studied. The asymptotic orders ofaverage sampling numbers of a Sobolev space on the sphere with aGaussian measure in the Lq(sd-1) metric for 1≤q≤∞ are obtained, and it is shown that some worst-caseasymptotically optimal algorithms are also asymptotically optimal in the average case setting inthe Lq(sd-1) metric for 1≤q≤∞.
	TO cite this article:HUANG Zexia,WANG He-Ping. Optimal recovery of functions on the sphere on a Sobolev spaces with a Gaussian measure in the average case setting[OL].[11 January 2013] http://en.paper.edu.cn/en_releasepaper/content/4514337

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