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基于任意给定的伸缩因子为a的正交多尺度函数, 给出一种提升其逼近阶的算法. 设Φ(x)=[φ1(x),x)=[φ2(x),…,φr(x)]T是伸缩因子为a,逼近阶为m的正交多尺度函数,则可以构造出一个重数为r+s,逼近阶为m+L(LÎZ+)的新正交多尺度函数Φnew(x)=ΦT(x),φr+1(x), φr+2(x),…, φr+s(x)T. 换言之, 通过增加多尺度函数的重数提升了它的逼近阶. 另外, 讨论了一个特殊情形:如果所给的正交多尺度函数Φ(x)=[φ1(x),φ2(x),…,φr(x)] T是对称的,则新构造的多尺度函数 Φnew(x)不仅能提升其逼近阶, 而且还保持对称性. 给出了若干构造算例. 相似文献
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广义Calderón Zygmund算子及其加权模不等式 总被引:2,自引:0,他引:2
本文推广Coifman和Meyer的Calderon-Zygmund算子概念,定义了M-型和θ-型广义Calderon-Zygmund算子,证明了它们的L~p有界性。然后对θ-型Calde-ron-Zygmund算子证明L~p加权模不等式。由于θ-型Calderon-Zygmund算子的广泛性,这就不但对已有的一些算子的加权模不等式给出了新的证明,同时还得到了一系列新的结果,其中包括各种类型的伪微分算子和交换子的加权模不等式。接着讨论具有较高阶光滑性条件的C~N-型Calderon-Zygmund算子,得到H~p到L~p有界性结果。最后通过把Calderon-Zygmund算子推广到向量值函数,并借助Little-wood-Paley理论,对Caifman和Meyer的一类广义伪微分算子和Meyer的一类广义伪微分算子得到加权模不等式。 相似文献
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Theoctonionalgebra,wedenoteit'byO,isanalternative,non-associativedivisionalgebrawiththebasicoctonionicunits:e0,e1,…,e6,e7,whileeoistheunitelementinO,satisfyingthatandtheconstatsop.p.,totallyantisymmetricinor,P,7,arenon-zeroandequalunityfortheClearly,thecommutator[e.,eo]~Zap.~.e.,atP,7=1,2,...t7.In1976,Habethashowedthat[Hab],ifonewishestogeneralizeclajssicaJfunctiontheorybyconsideringalgebra-valuedfunctionsinsuchwaythatausimple-Cauch}rformulastillholds,thenonehastorestricttoalgebraofcomplex… 相似文献
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PREDUAL SPACES FOR Q SPACES 总被引:2,自引:2,他引:0
To find the predual spaces Pα(R^n) of Qα(R^n) is an important motivation in the study of Q spaces. In this article, wavelet methods are used to solve this problem in a constructive way. First, an wavelet tent atomic characterization of Pα(Rn) is given, then its usual atomic characterization and Poisson extension characterization are given. Finally, the continuity on Pα of Calderon-Zygmund operators is studied, and the result can be also applied to give the Morrey characterization of Pα(Rn). 相似文献
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1 IntroductionThe only finite dimensional aIternative di.ili.,1 algebras over R are ffeal algebra R, Com-plex algebra C, Quaternion algebra H, Octonidn algebra O with the embedding relations:R G C C H g O. R and C are commutative and associative, H is associative but notcomlnutative, while O is neither commutative nor a.s..i.ti.e[1].Much earlier the great Swiss mathematician FUeter (a student of Hilbert) and hi8 studentsdeveloped Quaternion analysis up to l950.[2'3] and it was a great… 相似文献
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Let L=△Hn + V be a Schrdinger operator on Heisenberg group H n,where △Hn is the sublaplacian and the nonnegative potential V belongs to the reverse H¨older class BQ/2,where Q is the homogeneous dimension of H n.Let T1 =(△Hn + V)-1 V,T2 =(△Hn +V)-1/2 V 1/2,and T 3 =(△Hn +V)-1/2 Hn,then we verify that [b,Ti],i = 1,2,3 are bounded on some Lp(Hn),where b ∈ BMO(Hn).Note that the kernel of Ti,i=1,2,3 has no smoothness. 相似文献
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