Boundedness of Calderón-Zygmund operators with finite non-doubling measures

Let μ be a nonnegative Radon measure on ?d which satisfies the polynomial growth condition that there exist positive constants C₀ and n ∈ (0, d] such that, for all x ∈ ?d and r>0, μ(B(x, r))≤C0rn, where B(x, r) denotes the open ball centered at x and having radius r. In this paper, we show that, if μ(?d)<∞, then the boundedness of a Calderón-Zygmund operator T on L²(μ) is equivalent to that of T from the localized atomic Hardy space h¹(μ) to L^1,∞(μ) or from h¹(μ) to L¹(μ).     

齐次群上多线性奇异积分算子的有界性

Let G be a homogeneous group.In this paper,the author studies the boundedness of multi-sublinear operators on the product of weighted Lebesgue spaces on G.As its special case,the corresponding result of multilinear Calderón-Zygmund operators can be obtained.     

Toeplitz Type Operator Associated to Singular Integral Operator with Variable Kernel on Weighted Morrey Spaces

Suppose Tk,1 and Tk,2 are singular integrals with variable kernels and mixed homogeneity or ± I(the identity operator). Denote the Toeplitz type operator by Tb=∑Qk=1Tk,1MbTk,2,where Mbf=bf. In this paper, the boundedness of Tbon weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.     

广义Calderón-Zygmund算子的一个有界性结果

本文讨论了广义Ｃａｌｄｅｒóｎ－Ｚｙｇｍｕｎｄ算子的一个如下的有界性结果：∫Ｒｎ｜Ｔｆ（ｘ）｜ｗ（ｘ）ｄｘ≤Ｃ‖ｆ‖Ｈ１（Ｍｗ）,其中Ｔ是广义Ｃａｌｄｅｒóｎ－Ｚｙｇｍｕｎｄ算子,Ｍ是Ｈａｒｄｙ－Ｌｉｔｌｅｗｏｏｄ极大算子,ｗ是权函数,Ｈ１（μ）是一类Ｈａｒｄｙ型空间     

Calderón-Zygmund型算子交换子的加权尖锐估计

本文讨论了θ-型Calderón-Zygmund算子与BMO函数生成的交换子的加权估计.在权函数仅为非负局部可积函数或属于A∞的假设下,当0相似文献   

强度1二元正交阵列计数

利用Pólya计数理论给出强度1二元正交阵列计数公式.     

如何求解同分异构体计数问题

用浅显的方法具体实例化地介绍了求解同分异构体计数问题的图论及群论的数学抽象表示和数学原理,以及从生成函数及树型结构计数的概念到结构异构和立体异构两类同分异构体计数问题的求解。最后通过数学软件Maple16的简单编程,给出了具体实现的方法。     

烃同分异构体的计数

能否系统精确地解决高中化学学习中的同分异构体计数问题?本文在高中数学化学的背景知识之上,引入生成函数以及Pólya计数定理,在不考虑立体异构的前提下,从烷基的同分异构体计数入手,逐步推导烷烃、一烯烃、一炔烃苯的衍生物、二取代烷烃以及二烯烃的同分异构体计数的公式,并将计算结果与手工枚举进行对比,进一步证明其正确性。我们还归纳性地发掘了同分异构体计数的渐进特征并提出了以上烃类同分异构体计数的近似公式。对比国外的成果,本文尽力避免引入过多的数学概念,降低门槛,适合高中生阅读,加深对于烃结构的理解,培养计算思维;对比国内相同主题的研究,本文的推导形式清晰简洁,拓展性较强。     

A Weighted Weak Type Endpoint Estimate for the Multilinear Calderón-Zygmund Operators and Its Applications

A weighted weak type endpoint estimate is established for the m-linear operator with Calderón-Zygmund kernel,which was introduced by Coifman and Meyer.As applications,the mapping properties on weighted L~(P1)(R~n)×…×L~(Pm)(R~n)with weight MBω for certain maximal operator MB and general weight ω,and a two-weight weighted norm estimate for this operator,are obtained.     

Multi-weight, Weighted Weak Type Estimates for the Multilinear Calderón-Zygmund Operators

Let m be an integer and T be an m-linear Calderón-Zygmund operator, u, v1,..., vm be weights. In this paper, the authors give some sufficient conditions on the weights (u, vk) with 1 ≤ k ≤ m, such that T is bounded from Lp1(Rn, v1) × ··· × Lpm(Rn, vm) to Lp,∞(Rn, u).