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On Marcinkiewicz Integrals Associated to Compound Mappings with Rough Kernels

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Acta Mathematica Sinica,English Series 2014年第7期30卷 1210-1230页

作者： Feng LIU huo xiong wu School of Mathematical Sciences Xiamen University

The Lp bounds for the parametric Marcinkiewicz integrals associated to compound mapq pings, which contain many classical surfaces as model examples, are given, where the kernels of our operators are rather rough on the unit sphere as well as in the radial direction. These results substan- tially improve and extend some known results.

关键词： Marcinkiewicz integrals compound mappings rough kernels Fourier transform estimates,extrapolation

Weighted Oscillation and Variation Inequalities for Singular Integrals and Commutators Satisfying Hrmander Type Conditions

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Acta Mathematica Sinica,English Series 2017年第10期33卷 1397-1420页

作者： Jing ZHANG huo xiong wu School of Mathematics and Statistics Yili Normal College Yining 835000 P. R. China School of Mathematical Sciences Xiamen University Xiamen 361005 P. R. China

This paper is devoted to investigating the weighted LP-mapping properties of oscillation and variation operators related to the families of singular integrals and their commutators in higher dimension. We establish the weighted type （p, p） estimates for 1 〈 p 〈 ∞ and the weighted weak type （1, 1） estimate for the oscillation and variation operators of singular integrals with kernels satisfying certain HSrmander type conditions, which contain the Riesz transforms, singular integrals with more general homogeneous kernels satisfying the Lipschitz conditions and the classical Dini＇s conditions as model examples. Meanwhile, we also obtain the weighted LP-boundeness for such operators associated to the family of commutators generated by the singular integrals above with BMO（Rd）-functions.

关键词： Oscillation variation singular integrals commutators BMO functions HSrmander con-ditions Muckenhoupt weights

Rough Marcinkiewicz Integrals with Mixed Homogeneity on Product Spaces

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Acta Mathematica Sinica,English Series 2013年第7期29卷 1231-1244页

作者： Feng LIU huo xiong wu School of Mathematical Sciences Xiamen University

In this paper, the parabolic Marcinkiewicz integral operators on the product spaces R^m × R^n（m, n ≥ 2） are studied. The LP-boundedness for such operators are established under rather weak size conditions of the k... 详细信息

关键词： Marcinkiewicz integrals non-isotropic dilations maximal functions rough kernels product spaces

The Commutators of Strongly Singular Integral Operators on the Weighted Hardy Spaces

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Acta Mathematica Sinica,English Series 2021年第12期37卷 1909-1920页

作者： Yan Yan HAN huo xiong wu School of Mathematical Sciences Xiamen UniversityXiamen 361005P.R.China

Let T be a strongly singular Calderon-Zygmund operator and b∈L_(loc)(R^(n)).This article finds out a class of non-trivial subspaces BMO_(ω,p,u)(R^(n))of BMO(R^(n))for certain ω∈A_(1),0 详细信息

Let T be a strongly singular Calderon-Zygmund operator and b∈L_(loc)(R^(n)).This article finds out a class of non-trivial subspaces BMO_(ω,p,u)(R^(n))of BMO(R^(n))for certain ω∈A_(1),0

关键词： Strongly singular Calderon-Zygmund operators commutators Muckenhoupt weights BMO spaces Hardy spaces

On Rough Marcinkiewicz Integrals along Surfaces

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Acta Mathematica Sinica,English Series 2010年第4期26卷 717-730页

作者： huo xiong wu Jian Kai XU School of Mathematical Sciences Xiamen University Xiamen 361005 P. R. China

In this paper, the authors establish the LP-mapping properties of certain classes of Marcinkiewicz integral operators along surfaces with rough kernels. The results in this paper essentially extend as well as improve ... 详细信息

关键词： Marcinkiewicz integrals surfaces maximal operator Hardy space rough kernel

On Multiple Singular Integrals along Polynomial Curves with Rough Kernels

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Acta Mathematica Sinica,English Series 2008年第2期24卷 177-184页

作者： huo xiong wu Shan Zhi YANG School of Mathematical Sciences Xiamen University Xiamen 361005 P. R. China

This paper is devoted to the study of a class of singular integral operators defined by polynomial mappings on product domains. Some rather weak size conditions, which imply the Lp boundedness of these singular integral operators as well as the corresponding maximal truncated singular integral operators for some fixed 1〈p〈 ∞,are given.

关键词： singular integral product domain rough kernel Littlewood-Paley theory Fourier transform estimate

L^p Bounds for Singular Integrals with Rough Kernels on Product Domains

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Acta Mathematica Sinica,English Series 2012年第1期28卷 133-144页

作者： Li MA Da Shan FAN huo xiong wu School of Mathematics and Computer Sciences Gannan Normal UniversityGanzhou 341000P.R.China Department of Mathematics University of Wisconsin-MilwaukeeMilwaukeeWI 53201USA School of Mathematical Sciences Xiamen UniversityXiamen 361005P.R.China

This paper is concerned with singular integral operators on product domains with rough kernels both along radial direction and on spherical surface. Some rather weaker size conditions, which imply the L^P-boundedness ... 详细信息

关键词： Singular integral rough kernel product domain Littlewood-Paley theory Fourier transform estimate

Maximal Operators and Singular Integrals with Non-Isotropic Dilation on Product Domains

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Acta Mathematica Sinica,English Series 2010年第10期26卷 1847-1864页

作者： Zhong Kai LI Bo Lin MA huo xiong wu School of Mathematical Sciences Capital Normal University Beijing 100037 P. R. China College of Mathematics and Information Engineering Jiaxing University Jiaxing 314001 P. R. China School of Mathematical Sciences Xiamen University Xiamen 361005 P. R. China

In this paper, the authors study the with non-isotropic dilation on product domains. LP-mapping properties of certain maximal operators As an application, the LP-boundedness of the corre- sponding nomisotropic multiple singular integral operator is also obtained. Here the integral kernel functions Ω belong to the spaces L（logL）a（E1 × E2） for some a 〉 0, which is optimal.

关键词： Non-isotropic singular integral maximal function product domain rough kernel

Effect of stress-relief annealing on thermal fatigue cracks for die-casting die steels

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Journal of Iron and Steel Research International 2024年第5期31卷 1164-1176页

作者： Zhi-xiong Bai Xiao-chun wu School of Materials Science and Engineering Shanghai UniversityShanghai200444China

The effect of stress-relief annealing at different stages of thermal fatigue tests on crack growth was investigated using a self-built thermal cycle *** results showed that annealing could limit crack expansion *** reduced dislocation density and released the accumulation of residual *** addition,the strain accumulation in carbides was reduced by this *** was also found that double annealing was even more effective at inhibiting crack expansion compared to single stress-relief *** 1000 cycles,the maximum crack length was reduced by 31.1%and 45.2%for the samples after using the optimal single and double annealing processes,*** single stress-relief annealing,earlier annealing provides more benefit in delaying crack ***,effective double stress-relief annealing requires a suitable time interval between the annealing ***,after 800 cycles,surface hardness decreased significantly accompanied by an increase in the size and number of carbides,and cracks expanded predominantly along grain boundaries.

关键词： Thermal fatigue Steel Carbide Stress-relief annealing Dislocation Residual stress