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BOUNDEDNESS AND COMPACTNESS FOR THE COMMUTATOR OF THEω-TYPE CALDER′ON-ZYGMUND OPERATOR ON LORENTZ space

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Acta Mathematica Scientia 2023年第4期43卷 1587-1602页

作者：陶祥兴曾媛喻晓 Department of Mathematics Zhejiang University of Science and TechnologyHangzhou 310023China Department of Mathematics Shangrao Normal UniversityShangrao 334001China

In this paper,the authors consider theω-type Calder´on-Zygmund operator T_(ω)and the commutator[b,T_(ω)]generated by a symbol function b on the Lorentz space L^(p,r)(X)over the homogeneous space(X,d,μ).The boundedness and the compactness of the commutator[b,T_(ω)]on Lorentz space L^(p,r)(X)are founded for any p∈(1,∞)and r∈[1,∞).

关键词： ω-type Calder´on-Zygmund operator commutators Lorentz space homogeneous space

Classical Fourier Analysis over homogeneous spaces of Compact Groups

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Analysis in Theory and Applications 2016年第4期32卷 339-354页

作者： Arash Ghaani Farashahi Numerical Harmonic Analysis Group (NuHAG) Faculty Mathematics University of Vienna

This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G and μ be the normalized G-invariant measure on G/H associated to the Weil＇s formula. Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space L^2 （G / H, μ）.

关键词： Compact group homogeneous space dual space Fourier transform Plancherel(trace) formula Peter-Weyl Theorem

homogeneous Einstein-like metrics on symmetric spaces

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Science China Mathematics 2021年第5期64卷 1045-1060页

作者： Chao Qian Ail Wu School of Mathematics and Statistics Beijing Institute of TechnologyBeijing 102488China

In this paper, we study homogeneous Einstein-like metrics on the compact irreducible symmetric space M, which is not isometric to a compact Lie group and has rank greater than 1. Whenever there exists a closed proper subgroup G′ of G = Isom_0(M) acting transitively on M, we find all the G′-invariant A-metrics and B-metrics on M. More precisely, we prove that G′-invariant metrics on M must be A-metrics, and G′-invariant B-metrics on M are always Einstein.

关键词： homogeneous space symmetric space Einstein-like metric A-metric B-metric

COMMUTATORS OF BMO FUNCTIONS AND SINGULAR INTEGRAL OPERATORS WITH NON-SMOOTH KERNELS ON spaceS OF homogeneous TYPE OF FINITE MEASURE

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Analysis in Theory and Applications 2006年第1期22卷 41-55页

作者： Donggao Deng Yanbo Xu Lixin Yan Zhongshan University China Huaihai Institute of Technology China

Let X be a space of homogeneous type with finite measure. Let T be a singular integral operator which is bounded on L^p （X）, 1 〈 p 〈 ∞. We give a sufficient condition on the kernel k（x,y） of Tso thatwhen a function b ∈ BMO （X）,the commutator [b,T] （f）=T （b f）- bT （f） is bounded on spaces L^p for all p, 1 〈 p 〈 ∞.

关键词： commutator homogeneous space BMO function singular integral operator

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群作用在复几何中的一些运用

Chinese Quarterly Journal of Mathematics 2023年第3期38卷 254-275页

作者： GUAN Daniel School of Mathematics and Statistics Henan UniversityKaifeng 475004China Department of Mathematics University of California at RiversideCA 92521U.S.A.

In this article,we give a further survey of some progress of the applications of group actions in the complex geometry after my earlier survey around 2020,mostly related to my own interests.

关键词： Invariant structure homogeneous space Fiber bundles Hermitian manifolds Reductive Lie group Compact manifolds Chern class Co-homogeneity one Kahler manifolds

关于复几何中的一些新进展--与齐性流形相关领域

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Chinese Quarterly Journal of Mathematics 2020年第2期35卷 111-144页

作者：关庄丹 School of Mathematics and Statistics Henan UniversityKaifeng 475004China Department of Mathematics University of California at Riverside RiversideCA 92521 U.S.A.

In this article,we give a survey of some progress of the complex geometry,mostly related to the Lie group actions on compact complex manifolds and complex homogeneous spaces in the last thirty *** particular,we explore some works in the special area in Di erential Geometry,Lie Group and Complex homogeneous *** with the special area in nonlinear analysis on complex manifolds,they are the two major aspects of my research interests.

关键词： Invariant structure homogeneous space Complex torus bundles Hermitian manifolds Reductive Lie group Compact manifolds Ricci form Locally conformal Kahler manifolds