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L^p MIXED-NORM ESTIMATES FOR CONVOLUTION OPERATOR DEFINED BY SINGULAR MEASURES
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作者 Meifang Cheng Lisheng Shu 《Analysis in Theory and Applications》 2008年第1期50-54,共5页
Let F be a C^∞ curve in IR^n and μ be the measure induced by Lebesgue measure on F, multiplied by a smooth cut-off function. In this paper, we will prove some mixednorm estimates based on the average decay estimates... Let F be a C^∞ curve in IR^n and μ be the measure induced by Lebesgue measure on F, multiplied by a smooth cut-off function. In this paper, we will prove some mixednorm estimates based on the average decay estimates of the Fourier transform of μ. 展开更多
关键词 mixed-norm estimate singular measure complex interpolation theorem con-volution operator
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Singular Measures and Convolution Operators
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作者 J.M.ALDAZ JuanL.VARONA 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第3期487-490,共4页
We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type (1, 1) inequalities. As an application, we prove th... We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type (1, 1) inequalities. As an application, we prove that the best constants for the centered Hardy-Littlewood maximal operator associated with parallelotopes do not decrease with the dimension. 展开更多
关键词 Hardy-Littlewood maximal function Weak type inequalities singular measures Convo-lution operators
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FOURIER TRANSFORMATION AND SINGULAR INTEGRALS ON SELF-SIMILAR MEASURE
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作者 Wu Baoyi Su Weiyi, Nanjing University, China Department of Mathematics Nanjing University Nanjing 210093 PRC 《Analysis in Theory and Applications》 1998年第4期102-114,共13页
This paper serves two purposes. One is to modify Strichartz's results with respect to the asymptotic averages of the Fourier transform of μ on , self-similar measure defined by Hutchinson. Another purpose is to c... This paper serves two purposes. One is to modify Strichartz's results with respect to the asymptotic averages of the Fourier transform of μ on , self-similar measure defined by Hutchinson. Another purpose is to consider a singular integral operator on μ and show that this op- erator is of type (p,p)(1<p<∞). 展开更多
关键词 SHOW FOURIER TRANSFORMATION AND singular INTEGRALS ON SELF-SIMILAR measure MATH APPI
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SOME ASYMPTOTIC PROPERTIES OF THE CONVOLUTION TRANSFORMS OF FRACTAL MEASURES
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作者 曹丽 《Acta Mathematica Scientia》 SCIE CSCD 2012年第6期2096-2104,共9页
We study the asymptotic behavior near the boundary of u(x, y) = Ky * μ (x), defined on the half-space R^+ x RN by the convolution of an approximate identity Ky (.) (y 〉 0) and a measure μ on IRN. The Pois... We study the asymptotic behavior near the boundary of u(x, y) = Ky * μ (x), defined on the half-space R^+ x RN by the convolution of an approximate identity Ky (.) (y 〉 0) and a measure μ on IRN. The Poisson and the heat kernel are unified as special cases in our setting. We are mainly interested in the relationship between the rate of growth at boundary of u and the s-density of a singular measure μ. Then a boundary limit theorem of Fatou's type for singular measures is proved. Meanwhile, the asymptotic behavior of a quotient of Kμ and Ku is also studied, then the corresponding Fatou-Doob's boundary relative limit is obtained. In particular, some results about the singular boundary behavior of harmonic and heat functions can be deduced simultaneously from ours. At the end, an application in fractal geometry is given. 展开更多
关键词 fractal density harmonic function CONVOLUTION singular measure
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A Riesz Product Type Measure on the Cantor Group
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作者 SHI QI-YAN 《Communications in Mathematical Research》 CSCD 2010年第1期7-16,共10页
A Riesz type product as Pn=nЛj=1(1+awj+bwj+1)is studied, where a, b are two real numbers with |a| + |b| 〈 1, and {wj} are indepen- dent random variables taking values in (-1, 1} with equal probability. Le... A Riesz type product as Pn=nЛj=1(1+awj+bwj+1)is studied, where a, b are two real numbers with |a| + |b| 〈 1, and {wj} are indepen- dent random variables taking values in (-1, 1} with equal probability. Let dw be the normalized Haar measure on the Cantor group Ω = (-1, 1}^N. The sequence of P,~dw 1 probability measures {Pndw/E(Pn) } is showed to converge weakly to a unique continuous measure on/2, and the obtained measure is singular with respect to dw. 展开更多
关键词 Riesz product Cantor group weak topology singularity of measure 2000 MR subject classification- 42A55 28A33
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Stability of Singular and Time-Delay Measure Differential Large-Scale Systems with Impulse Effects
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作者 GUAN Zhihong LIU Yongqing(Department of Automation,South China University of Technology,Guangzhou 510641) 《Systems Science and Systems Engineering》 CSCD 1994年第1期74-82,共9页
This paper is devoted to the investigation of stability for singular and time-delay measure differential large scale systems with impulsive solution.With the help of Drazin inverse,the variation of parameters formula ... This paper is devoted to the investigation of stability for singular and time-delay measure differential large scale systems with impulsive solution.With the help of Drazin inverse,the variation of parameters formula of large scale singular systems containing measures and delays is obtained.Employing inequality methods and comparison theory,the stability properties of large scale systems are studied. 展开更多
关键词 singular measure large scale systems DELAYS impulsive solution STABILITY
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A new steering approach for VSCMGs with high precision 被引量:3
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作者 Huang Xinghong Jia Yinghong +1 位作者 Xu Shijie Huang Tingxuan 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2016年第6期1673-1684,共12页
A new variable speed control moment gyro(VSCMG) steering law is proposed in order to achieve higher torque precision. The dynamics of VSCMGs is established, and two work modes are then designed according to command to... A new variable speed control moment gyro(VSCMG) steering law is proposed in order to achieve higher torque precision. The dynamics of VSCMGs is established, and two work modes are then designed according to command torque: control momentum gyro(CMG)/reaction wheel(RW) hybrid mode for the large torque case and RW single mode for the small. When working in the CMG/RW hybrid mode, the steering law deals with the gimbal dead-zone nonlinearity through compensation by RW sub-mode. This is in contrast to the conventional CMG singularity avoidance and wheel speed equalization, as well as the proof of definitely hyperbolic singular property of the CMG sub-mode. When working in the RW single mode, the motion of gimbals will be locked. Both the transition from CMG/RW hybrid mode to RW single mode and the reverse are studied. During the transition, wheel speed equalization and singularity avoidance of both the CMG and RW submodes are considered. A steering law for the RWs with locked gimbals is presented. It is shown by simulations that the VSCMGs with this new steering law could reach a better torque precision than the normal CMGs in the case of both large and small torques. 展开更多
关键词 Attitude control Dead-zone nonlinearity Integrated singularity measurement singularity avoidance Variable speed control moment gyros(VSCMGs) Wheel speed equalization
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Geometry and Hardy spaces on spaces of homogeneous type in the sense of Coifman and Weiss 被引量:2
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作者 HAN YanChang HAN YongSheng LI Ji 《Science China Mathematics》 SCIE CSCD 2017年第11期2199-2218,共20页
It is known that the space of homogeneous type introduced by Coifman and Weiss(1971) provides a very natural setting for establishing a theory of Hardy spaces. This paper concentrates on how the geometrical conditions... It is known that the space of homogeneous type introduced by Coifman and Weiss(1971) provides a very natural setting for establishing a theory of Hardy spaces. This paper concentrates on how the geometrical conditions of the space of homogeneous type play a crucial role in building a theory of Hardy spaces via the Littlewood-Paley functions. 展开更多
关键词 spaces of homogeneous type Hardy space singular integrals Carleson measure space BMO
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Homogeneous wavelets and framelets with the refinable structure 被引量:1
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作者 HAN Bin 《Science China Mathematics》 SCIE CSCD 2017年第11期2173-2198,共26页
Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, no... Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets and framelets enjoy many desirable theoretical properties and are often intrinsically linked to the refinable structure and multiresolution analysis. In this paper, we provide a comprehensive study on connecting homogeneous wavelets and framelets to nonhomogeneous ones with the refinable structure. This allows us to understand better the structure of homogeneous wavelets and framelets as well as their connections to the refinable structure and multiresolution analysis. 展开更多
关键词 homogeneous wavelets and framelets nonhomogeneous wavelets and framelets refinable structure shift-invariant spaces multiresolution analysis Schur decomposition for Hermite matrices of measurable functions singular value decomposition for matrices of measurable functions
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