共查询到19条相似文献,搜索用时 62 毫秒
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本文定义了R^n中的某类区域的边界上的Cauchy奇异积分,证明了这种奇异分具有与复情形时有类似的边界性质,在边界是C′光滑的条件下我们明Plemelj公式和Privalov定理。一些结论是新的而另一些改进前人的工作。 相似文献
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积域上的一类粗糙奇异积分算子 总被引:4,自引:0,他引:4
本文讨论了积域Rn×Rm上一类带粗糙核的奇异积分算子Tf(x,y)=p.v.Rn×RmΩ(u,v)|u|n|v|mh(|u|,|v|)f(x-u,y-v)dudv的Lp(Rn×Rm)有界性.这里,Ω为原子Hardy空间H1a(Sn-1×Sm-1)中的函数且h为空间l∞(Lq)(R+×R+)中的径向函数. 相似文献
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对与具有一般核的分数次奇异积分算子相关的Toeplitz型算子,本文证明了其sharp极大函数不等式,作为应用,得到了该算子在Lebesgue空间,Morrey空间和Triebel-Lizorkin空间的有界性. 相似文献
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本文讨论开口曲线上奇异积分算子的稳定性、端点行为和可逆性关系,证明了当曲线的端点为非特异节点时这类奇异积分算子是稳定的, 对该类算子在端点的性态进行了确切描述, 以及通过对奇异积分算子相互关系的分析,给出了算子在其上可逆的函数空间或函数集以及对应的 逆映射. 同时,文章列举了上述性质在奇异积分方程方面的一些应用. 相似文献
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On the basis of the Cauchy integral formulas for regular and biregular functions, we define some Cauchy-type singular integral operators. Then we discuss the Hlder continuous property of some singular integral operators with one integral variable. Then we divide a singular integral operator with two variables into three parts and prove its Hlder continuous property on the boundary. 相似文献
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假设A是一个Young函数,MD#为广义sharp极大函数.本文首先引进了LA-Hrmander条件,对于满足LA-Hrmander条件的算子T,得到了与T相关的广义sharp极大函数的估计.然后,再利用该估计得到了算子T的加权Lp范数被Hardy-Littlewood极大函数和与Aˉ相关的极大函数的加权Lp范数所控制(0
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We prove an interpolation type inequality between , and spaces and use it to establish the local Hölder continuity of the inverse of the -Laplace operator: , for any and in a bounded set in .
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E. B. Fabes M. V. Safonov Yu Yuan 《Transactions of the American Mathematical Society》1999,351(12):4947-4961
A boundary backward Harnack inequality is proved for positive solutions of second order parabolic equations in non-divergence form in a bounded cylinder which vanish on , where is a bounded Lipschitz domain in . This inequality is applied to the proof of the Hölder continuity of the quotient of two positive solutions vanishing on a portion of
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In this paper,a new reverse extended Hardy's integral inequality is proved by means of weight coefficients and the technique of real analysis.Some particular results are considered. 相似文献
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关于积域上的粗糙奇异积分算子的一点注记 总被引:5,自引:0,他引:5
讨论积域上的奇异积分算子:TΩf(x,y) = p.v.∫Rn×RmΩ(u,v)|u|n|v|m f(x - u,y - v)dudv的Lp 有界性,及相应的Marcinkiew icz积分的L2 有界性. 其中Ω为类似文[4]中引进的函数类. 相似文献
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讨论了实 Clifford分析中的一类高阶奇异积分 ,给出了这类高阶奇异积分的递推公式 ,计算公式 ,并且研究了这类高阶奇异积分的 Hlder连续性 ,从而使实 Clifford分析理论得以拓展 . 相似文献
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In this paper,we consider the strong dissipative KDV type equation on an unbounded domain R1.By applying the theory of decomposing operator and the method of constructing some compact operator in weighted space,the existence of exponential attractor in phase space H2(R1) is obtained. 相似文献
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Nam-Gyu Kang 《Journal of the American Mathematical Society》2007,20(1):185-210
We show that the normalized (pre-)Schwarzian derivative of SLE, after we subtract a negligible term, is a complex BMO martingale. Its BMO norm gives strong evidence for Duplantier's duality conjecture. We also show that it has correlations that decay exponentially in the hyperbolic distance.
We reexamine S. Rohde and O. Schramm's derivative expectation to derive the conjectured sharp estimate for the Hölder exponent unless the parameter of SLE is 4.