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On the maximal operator Associated with Certain Rotational Invariant Measures

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Acta Mathematica Sinica,English Series 2010年第6期26卷 993-1004页

作者： Adrián INFANTE Fernando SORIA Department of Mathematics Universidad Simn Bolívar Department of Mathematics Universidad Autnoma de Madrid

The aim of this work is to investigate the integrability properties of the maximal operator Mu,associated with a non-doubling measure μ defined on Rn. We start by establishing for a wide class of radial and increasing measures μ that Mu is bounded on all the spaces Lu^p（R^n）,P〉***,we show that there is a radial and increasing measure p for which Mμ does not map Lμ^p（R^n） into weak Lμ^p（R^n）,1≤p〈∞.

关键词： maximal operator non-doubling measures

Weighted Inequalities for the Generalized maximal operator in Martingale Spaces

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Chinese Annals of Mathematics,Series B 2011年第5期32卷 781-792页

作者： Wei CHEN Peide LIU School of Mathematical Sciences Yangzhou University Yangzhou 225002 Jiangsu China School of Mathematics and Statistics Wuhan University Wuhan 430072 China

The generalized maximal operator .44 in martingale spaces is considered. For 1 〈 p ≤ q 〈 ∞, the authors give a necessary and sufficient condition on the pair （μ, v） for M to be a bounded operator from martingale space L^P（μ） into L^q（μ） or weak-L^q（μ）, where μ is a measure on Ω × N and v a weight on Ω. Moreover, the similar inequalities for usual maximal operator are discussed.

关键词： Martingale maximal operator Weighted inequality Carleson measure

WEAK TYPE INEQUALITY FOR THE maximal operator OF WALSH-KACZMARZ-MARCINKIEWICZ MEANS

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Acta Mathematica Scientia 2016年第2期36卷 359-370页

作者： Ushangi GOGINAVA Karoly NAGY Department of Mechanics and Mathematics Tbilisi State University Chavchavadze str. 1 Tbilisi 0128 Georgia Institute of Mathematics and Computer Sciences College of Nyiregyhdza SSstSi str. 31/B 4400 Nyiregyhdza Hungary

The main aim of this article is to prove that the maximal operator σ^k＊ of the Marcinkiewicz-Fejer means of the two-dimensional Fourier series with respect to Walsh- Kaczmarz system is bounded from the Hardy space H... 详细信息

关键词： Walsh-Kaczmarz system Marcinkiewicz-Fej^r means maximal operator a.e.convergence weak type inequality

Weighted Estimates for the maximal Commutator of Singular Integral operator on Spaces of Homogeneous Type

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Communications in Mathematical Research 2010年第1期26卷 53-66页

作者： ZHANG HAO Department of Applied Mathematics Information Engineering University Zhengzhou 450002

Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associated kernel satisfies the HSlder condition on the first variable and some condition which is fairly weaker than the Holder condition on the second variable.

关键词： spaces of homogeneous type weighted estimates singular integral operator commutator maximal operator

Some maximal operators Related to Families of Singular Integral operators

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Acta Mathematica Sinica,English Series 2004年第3期20卷 441-452页

作者： HanXU DaShanFAN MengWANG DepartmentofInformationandComputingScience ZhejiangInstituteo.fScienceandTechnologyHangzhou310018P.R.China DepartmentofMathematics UniversityofWisconsin-MilwaukeeMilwaukeeWI53201USA DepartmentofMathematics ZhejiangUniversitry(XixiCampus)Hangzhou310028P.R.China

In this paper, we shall study L p -boundedness of two kinds of maximal operators related to some families of singular integrals.

关键词： maximal operator Singular integral Littlewood–Paley theory L p -boundedness

Dimension of divergence sets for dispersive equation

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Frontiers of Mathematics in China 2020年第2期15卷 317-331页

作者： Senhua LAN Tie LI Yaoming NIU College of Mathematics Physics and Information EngineeringJiaxing UniversityJiaxing 314001China Faculty of Mathematics Baotou Teachers’College of Inner Mongolia University of Science and TechnologyBaotou 014030China

Consider the generalized dispersive equation defined by{iδtu+Ф(√-△)u=0,(x,t)∈R^n×R,u(x,0)=f(x),F∈F(R^n),(*)whereФ(√-△)is a pseudo-differential operator with symbolФ(|ζ|).In the present paper,assuming thatФsatisfies suitable growth conditions and the initial data in H^s(R^n),we bound the Hausdorff dimension of the sets on which the pointwise convergence of solutions to the dispersive equations(*)*** upper bounds of Hausdorff dimension shall be obtained via the Kolmogorov-Seliverstov-Plessner method.

关键词： Dispersive equation Hausdorff dimension maximal operator

Estimates for the maximal Bilinear Singular Integral operators

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Acta Mathematica Sinica,English Series 2015年第5期31卷 847-862页

作者： Guo En HU Department of Applied Mathematics Zhengzhou Information Science and Technology Institute

In this paper, the behavior on the product of Lebesgue spaces is considered for the maximal operators associated with the bilinear singular integral operators whose kernels satisfy certain minimal regularity conditions.

关键词： Bilinear singular integral operator maximal operator multilinear interpolation Calderon-Zygmund decomposition

THE BOUNDEDNESS OF MULTILINEAR COMMUTATORS ON WEIGHTED SPACES AND HERZ-TYPE SPACES

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Acta Mathematica Scientia 2007年第2期27卷 361-372页

作者：周伟军马柏林徐景实 College of Mathematics and Computational Science Changsha University of Science and Technology College of Mathematics and Econometrics Hunan University Department of Mathematics Hunan Normal University

The boundedness of maximal multilinear commutator on certain weighted spaces is obtained. The boundedness of mulitilinear commutators of singular integrals with Calderon-Zygmund kernel on Herz-type spaces is also cons... 详细信息

关键词： Commutator maximal operator Herz space singular integral

SEVERAL WEAK-TYPE WEIGHTED INEQUALITIES IN ORLICZ MARTINGALE CLASSES

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Acta Mathematica Scientia 2011年第3期31卷 1041-1050页

作者：陈伟刘培德 School of Mathematical Sciences Yangzhou University School of Mathematics and Statistics Wuhan University

The aim of this paper is to establish several necessary and sufficient conditions in order that the weighted inequality ρ（M f 〉 λ）Φ（λ） ≤ C ∫_Ω~Ψ （C｜f｜）σdμ,λ 〉 0 or ρ（Mf〉λ） ≤ C∫-Ω~Φ（Cλ^-1 ｜f｜）σdμ,λ 〉0 holds for every uniformly integral martingale f=（f_n）, where M is the Doob＇s maximal operator, Φ, Ψ are both Φ-functions, and e, σ are weights.

关键词： martingale space maximal operator weighted inequality Orlicz norm