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	1. Boundedness and compactness of multilinear singular integrals on Morrey spaces
	MEI Ting,LI Ao-Bo
	Mathematics 20 April 2023
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	Abstract:In this paper, we consider the boundedness and compactness of the multilinear singular integral operator on Morrey spaces, which is defined by\begin{align}T_Af(x)={\rm{p.v.}}\int_{\mathbb{R}^n} \frac{\Omega(x-y)}{\|x-y\|^{n+1}} R(A;x,y)f(y)dy,\end{align}where $R(A;x,y)=A(x)-A(y)-\nabla A(y)\cdot(x-y)$ with $D^\beta A\in BMO(\mathbb{R}^n)$ for all $\|\beta\|=1$.We prove that $T_A$ is bounded and compact on Morrey spaces $L^{p,\lambda}(\mathbb{R}^n)$ for all $1<p<\infty$ with $\Omega$ and $A$ satisfying some conditions. Moreover, the boundedness and compactness of the maximal multilinear singular integral operator $T_{A,*}$ on Morrey spaces are also given in this paper.
	TO cite this article:MEI Ting,LI Ao-Bo. Boundedness and compactness of multilinear singular integrals on Morrey spaces[OL].[20 April 2023] http://en.paper.edu.cn/en_releasepaper/content/4760244


	2. Littlewood-Paley Characterizations of Second-Order Sobolev Spaces via Averages on Balls
	HE ZIYI, YANG DACHUN, YUAN WEN
	Mathematics 02 October 2015
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	Abstract:In this paper, the authors characterize second-order Sobolev spaces $W^{2,p}({mathbb R}^n)$,with $pin [2,infty)$ and $ninmathbb N$ or $pin (1,2)$ and $nin{1,2,3}$, via the Lusin areafunction and the Littlewood-Paley $g_lambda^st$-function in terms of ball means.
	TO cite this article:HE ZIYI, YANG DACHUN, YUAN WEN. Littlewood-Paley Characterizations of Second-Order Sobolev Spaces via Averages on Balls[OL].[ 2 October 2015] http://en.paper.edu.cn/en_releasepaper/content/4656719

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	3. Weighted Endpoint Estimates for Commutators ofCalder'on-Zygmund Operators
	LIANG YIYU, KY LUONG DANG, YANG DACHUN
	Mathematics 02 October 2015
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	Abstract:Let $deltain(0,1]$ and $T$ be a $delta$-Calder'on-Zygmund operator.Let $w$ be in the Muckenhoupt class $A_{1+delta/n}({mathbb R}^n)$ satisfying$int_{{mathbb R}^n}rac {w(x)}{1+\|x\|^n},dx<infty$.When $bin{ m BMO}(mathbb R^n)$,it is well known that the commutator $[b, T]$ is not bounded from $H^1(mathbb R^n)$to $L^1(mathbb R^n)$ if $b$ is not a constant function.In this article, the authors find out a proper subspace${mathopmathcal{BMO}_w({mathbb R}^n)}$of $mathopmathrm{BMO}(mathbb R^n)$ such that,if $bin {mathopmathcal{BMO}_w({mathbb R}^n)}$, then $[b,T]$ is bounded from theweighted Hardy space $H_w^1(mathbb R^n)$ to the weighted Lebesguespace $L_w^1(mathbb R^n)$.Conversely, if $bin{ m BMO}({mathbb R}^n)$ and the commutators of theclassical Riesz transforms ${[b,R_j]}_{j=1}^n$are bounded from $H^1_w({mathbb R}^n)$ into $L^1_w(R^n)$,then $bin {mathopmathcal{BMO}_w({mathbb R}^n)}$.
	TO cite this article:LIANG YIYU, KY LUONG DANG, YANG DACHUN. Weighted Endpoint Estimates for Commutators ofCalder'on-Zygmund Operators[OL].[ 2 October 2015] http://en.paper.edu.cn/en_releasepaper/content/4656709


	4. 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


	5. 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


	6. 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


	7. 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


	8. 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


	9. 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


	10. 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

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