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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. Differential Harnack estimates for $r$-positive $(p, p)$-forms on Kähler manifolds
	Niu Yan-yan
	Mathematics 03 January 2017
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	Abstract:In this paper, we study the $(p, p)$-form solution to the Hodge Laplacian heat equation on a Kähler manifold. After establishing the preservation of $r$-positivity of such solution under some invariant curvature condition, %that the $r$-positivity of a $(p, p)$-form solution is preserved under some %invariant curvature condition, we prove a differential Harnack estimate (in the sense of Li-Yau-Hamilton) for the $r$-positive solutions of the Hodge Laplacian heat equation. We also prove a nonlinear version coupled with the Kähler-Ricci flow.
	TO cite this article:Niu Yan-yan. Differential Harnack estimates for $r$-positive $(p, p)$-forms on Kähler manifolds[OL].[ 3 January 2017] http://en.paper.edu.cn/en_releasepaper/content/4716395

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	3. Submanifolds of Cartan-Hartogs Domains and Complex Euclidean Spaces
	Cheng Xiao-Liang,Niu Yan-Yan
	Mathematics 03 January 2017
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	Abstract:In this paper, we study the non-existence of common submanifolds of a complex Euclidean space and a Cartan-Hartogs domain equipped with their canonical metrics.
	TO cite this article:Cheng Xiao-Liang,Niu Yan-Yan. Submanifolds of Cartan-Hartogs Domains and Complex Euclidean Spaces[J].


	4. Weak (1,1) boundedness for the higher order Christ-Journ'e commutator
	LAI Xudong,DING Yong
	Mathematics 30 October 2016
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	Abstract:A weak type $(1,1)$ estimate is established for the high order commutator introduced by Christ and Journ'e which is defined by[ T[a_1,cdots,a_l]f(x)=pv int K(x-y)(prod_{i=1}^lm_{x,y}a_i)cdot f(y)dy, ]where $m_{x,y}a_i=int_0^1a_i(sx+(1-s)y)ds$ and $K$ is the Calder'on-Zygmund convolution kernel on $mathbb{R}^d (dgeq2)$.
	TO cite this article:LAI Xudong,DING Yong. Weak (1,1) boundedness for the higher order Christ-Journ'e commutator[OL].[30 October 2016] http://en.paper.edu.cn/en_releasepaper/content/4708655


	5. $L^p$ compactess for Calder'on type commutators
	MEI Ting,DING Yong
	Mathematics 30 October 2016
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	Abstract:In this paper, we discuss the $L^p$ compactness of Calder'on type commutators $T_A$ defined byegin{align}T_Af(x)={ m p.v.}int_{R^n} rac{Omega(x-y)}{\|x-y\|^{n+1}} R(A;x,y)f(y)dy,end{align}where $R(A;x,y)=A(x)-A(y)- abla A(y)cdot(x-y)$ with $D^eta Ain BMO(R^n)$ for all $nge 2$ and $\|eta\|=1$, and $Omega$ is homogeneous of degree zero and has a vanishing moment of order one on $mathbb{S}^{n-1}$.We prove that both of $T_A$ and its maximal operator $T_{A,*}$ are compact operators on $L^p(R^n)$ for all $1<p<infty$ with $A$ satisfying some conditions. Moreover, the compactness of the fractional operators $I_{lpha,A,m}$ and $M_{lpha,A,m}$ are also given.
	TO cite this article:MEI Ting,DING Yong. $L^p$ compactess for Calder'on type commutators[OL].[30 October 2016] http://en.paper.edu.cn/en_releasepaper/content/4708652


	6. Nonuniform Sampling for Random Signals Bandlimited in the Linear Canonical Transform Domain
	HUO Haiye,SUN Wenchang
	Mathematics 21 May 2016
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	Abstract:The nonuniform sampling for random signals which are bandlimited in the linear canonical transform (LCT) domain is studied in this paper.It was shown that the nonuniform sampling for a random signal bandlimited in the LCT domainis equal to the uniform sampling in the sense of second order statistic characters after a pre-filter in the LCTdomain. Moreover, an approximate recovery approach for nonuniform sampling of random signals bandlimited in the LCT domain is proposed.Finally, the mean square error of the nonuniform sampling is studied.
	TO cite this article:HUO Haiye,SUN Wenchang. Nonuniform Sampling for Random Signals Bandlimited in the Linear Canonical Transform Domain[OL].[21 May 2016] http://en.paper.edu.cn/en_releasepaper/content/4690388


	7. Stable Recovery of Block Sparse Signals via Mixed $l_{p}/l_{q}$ Optimization Algorithm
	HUO Haiye,SUN Wenchang
	Mathematics 18 May 2016
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	Abstract:In this paper, the stable recovery of block sparse signals is investigated.A general mixed $l_{p}/l_{q}$ optimization algorithm is proposed, under which the block restricted isometry property (block RIP) and the block null space property (block NSP) are both shown to be sufficient conditions on a measurement matrix for stable recovery of block-sparse signals. Moreover, a new concept of the block sparse approximationproperty (block SAP) is defined in this paper. It is shown that the block SAP is also a sufficient condition on a measurement matrix for stably recovering block-sparse signals based on the mixed $l_{p}/l_{q}$ optimization algorithm. Finally, the relationship between the block SAP, the block RIP, and the block NSP are studied.
	TO cite this article:HUO Haiye,SUN Wenchang. Stable Recovery of Block Sparse Signals via Mixed $l_{p}/l_{q}$ Optimization Algorithm[OL].[18 May 2016] http://en.paper.edu.cn/en_releasepaper/content/4690394


	8. Lower Estimate of Widths of Sobolev Classes on Regular Hexagon
	YANG Wei, LIU Yongping
	Mathematics 12 May 2016
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	Abstract:As one of the classical approximation problems, n-widths on hexagon has been discussed in this paper. Firstly, the definitions of periodic function classes on regular hexagon and rectangle on the plane are given. And then their relationship is presented. Furthermore, taking advantage of this relationship the asymptotic lower estimates of the n-width of the class of $L_p$ in $L_q$ metric is obtained.
	TO cite this article:YANG Wei, LIU Yongping. Lower Estimate of Widths of Sobolev Classes on Regular Hexagon[OL].[12 May 2016] http://en.paper.edu.cn/en_releasepaper/content/4689837


	9. Relative $n$-widths of periodicdifferentiable function classes on the regular hexagon
	YANG Wei, LIU Yongping
	Mathematics 12 May 2016
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	Abstract:Widths theory is an essential part of the extremal theory of approximation. As a branch of widths, relative n-widths attracts the attention of researchers and has been studied a lot in resent years. In this paper, periodic function classes on regular hexagon and rectangle on the plane, and also their relationship have been considered first.Furthermore, using the iterate Laplace operator, a periodic differentiable class on regular hexagon is defined. Taking advantage of the relationship mentioned above, the asymptotic estimates of the relative n-width of the class of $L_2$ in $L_q$ metric is obtained.
	TO cite this article:YANG Wei, LIU Yongping. Relative $n$-widths of periodicdifferentiable function classes on the regular hexagon[OL].[12 May 2016] http://en.paper.edu.cn/en_releasepaper/content/4689834


	10. Abstract Hardy Spaces on product domains
	Gong Ru-Ming
	Mathematics 14 December 2015
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	Abstract:In this paper, we define the abstract Hardy spaces.And then we propose some general conditions which guaranteethe continuity from our Hardy space into $L^1$. At last,we give the definition of the ${ m BMO}$ space and studythe relationship between abstract Hardy spaces and ${ m BMO}$ space.
	TO cite this article:Gong Ru-Ming. Abstract Hardy Spaces on product domains[OL].[14 December 2015] http://en.paper.edu.cn/en_releasepaper/content/4671222

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