共查询到20条相似文献,搜索用时 46 毫秒
1.
首先给出了Heisenberg型群上一类仿积算子的定义,研究了该算子的L~2→L~2有界性.其次探讨了Heisenberg型群上的Calderon-Zygmund算子,包括该算子的L~p→L~p有界性,L~1→L~(1,∞)有界性以及H~1→L~1有界性.最后证明了仿积算子也是Calderon-Zygmund算子,同时还证明了仿积算子的一些其它重要性质. 相似文献
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本文证明了当α=n1-1q时,强奇异积分算子是从齐次加权Herz型Hardy空间HKα,pq(w1;w2)到齐次加权Herz空间Kα,pq(w1;w2)上的有界算子.而且,该算子在非齐次加权Herz型Hardy空间HKα,pq(w1;w2)上的有界性也被考查. 相似文献
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强奇异卷积算子交换子的Hardy型空间估计 总被引:2,自引:0,他引:2
本文给出了强奇异卷积算子交换子[6,T]在Hardy型空间中的估计,其中 b∈BMO(Rn)且一致连续, T为强奇异卷积算子. 相似文献
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讨论了Heisenberg群Hn上一类不变微分算子P=Σ↑m↓l=0alL^l的离散特征值的存在性。这里al〉0,l=0,1,…,m,m≥2。L为Hn上的sub-Laplace算子。我们通过建立向量场的Poincare型不等式,结合Friedrichs对欧氏空间上Laplace算子的方法,得到了存在性结果。 相似文献
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设 F是λ阶正则的齐次分布,-Q≤λ<0。作者研究了Heisenberg群上的算子g*F在加幂权的Lebesgue空间和Herz型 Hardy空间上的有界性,其中 g是一恰当的函数。而且,本文还得到了由BMO(H~n)函数和线性算子T所生成的交换子[b,T]在Herz空间上的有界性。 相似文献
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假设n和m是两个正整数,P(x,D)是定义在维数为n的紧致无边流形M上的一般m阶椭圆自伴微分算子.在一定条件下,本文主要证明微分算子P(x,D)的预解式的一致L^p-L^q估计,其中n〉m≥2,(p,q)在Sobolev线上并满足1/p-1/q=m/n,p≤2(n+1)/n+3,q≥2(n+1)/n-1.本文的一个核心引理是建立曲面Σx={ξ∈Tx^*(M):p(x,ξ)=1}上测度的Fourier变换衰减估计的具体表达式,并利用它来得到局部算子的一致L^p-L^q估计. 相似文献
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本文考虑多线性Fourier乘子算子在加权Lebesgue空间的乘积空间上的性质,利用多线性Fourier乘子算子的核估计以及多线性奇异积分算子的加权理论,建立多线性Fourier乘子算子的(关于多重Ap/r(R^mn)权函数以及关于一般权函数的)两个加权估计. 相似文献
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Let 0<p≤1<q<0, andw
1
,w
2
∈ A
1
(Muckenhoupt-class). In this paper the authors prove that the strongly singular convolution operators are bounded from the
homogeneous weighted Herz-type Hardy spacesH Kα, p
q(w1; w2) to the homogeneous weighted Herz spacesK
α, p
q
(w1; w2), provided α=n(1−1/q). Moreover, the boundedness of these operators on the non-homogeneous weighted Herz-type Hardy spacesH K
α, p
q
(w
1;w
2) is also investigated.
Supported by the National Natural Science Foundation of China 相似文献
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Giovanni Stegel 《Proceedings of the American Mathematical Society》2000,128(6):1807-1812
Consider a discrete group and a bounded self-adjoint convolution operator on ; let be the spectrum of . The spectral theorem gives a unitary isomorphism between and a direct sum , where , and is a regular Borel measure supported on . Through this isomorphism corresponds to multiplication by the identity function on each summand. We prove that a nonzero function and its transform cannot be simultaneously concentrated on sets , such that and the cardinality of are both small. This can be regarded as an extension to this context of Heisenberg's classical uncertainty principle.
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Neil Lyall 《Transactions of the American Mathematical Society》2007,359(9):4467-4488
We consider the mapping properties of a model class of strongly singular integral operators on the Heisenberg group ; these are convolution operators on whose kernels are too singular at the origin to be of Calderón-Zygmund type. This strong singularity is compensated for by introducing a suitably large oscillation.
Our results are obtained by utilizing the group Fourier transform and uniform asymptotic forms for Laguerre functions due to Erdélyi.
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Fulvio Ricci Giancarlo Travaglini 《Proceedings of the American Mathematical Society》2001,129(6):1739-1744
Let be a convex curve in the plane and let be the arc-length measure of Let us rotate by an angle and let be the corresponding measure. Let . Then This is optimal for an arbitrary . Depending on the curvature of , this estimate can be improved by introducing mixed-norm estimates of the form where and are conjugate exponents. 相似文献
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This paper firstly discusses the existence of strongly irreducible operators on Banach spaces. It shows that there exist strongly
irreducible operators on Banach spaces with w*-separable dual. It also gives some properties of strongly irreducible operators on Banach spaces. In particular, if T is a strongly irreducible operator on an infinite-dimensional Banach space, then T is not of finite rank and T is not an algebraic operator. On Banach spaces with subsymmetric bases, including infinite-dimensional separable Hilbert
spaces, it shows that quasisimilarity does not preserve strong irreducibility. In addition, we show that the strong irreducibility
of an operator does not imply the strong irreducibility of its conjugate operator, which is not the same as the property in
Hilbert spaces. 相似文献
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Peter Junghanns Lothar von Wolfersdorf 《Mathematical Methods in the Applied Sciences》2012,35(8):894-922
The paper deals with the monotonicity of singular integral operators of the form where is the Cauchy singular integral operator on the interval (0,1) of the real axis and q is a power or logarithmic function. Under suitable assumptions, such singular integral operators are proved to be monotone and maximal monotone in spaces with power weights. Moreover, two related integral equations with weakly singular kernels of logarithmic type are studied. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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Pingrun Li 《复变函数与椭圆型方程》2016,61(1):67-75
In this paper, we investigate two classes of linear equations of discrete convolution type with harmonic singular operator. Using the Laurent transform theory, we turn the above linear equations into Riemann boundary value problems. Then, the solutions of the equations are obtained in the class of Hölder continuous functions. 相似文献
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We consider a locally compact group and a limiting measure of a commutative infinitesimal triangular system (c.i.t.s.) of probability measures on . We show, under some restrictions on , or , that belongs to a continuous one-parameter convolution semigroup. In particular, this result is valid for symmetric c.i.t.s. on any locally compact group . It is also valid for a limiting measure which has `full' support on a Zariski connected -algebraic group , where is a local field, and any one of the following conditions is satisfied: (1) is a compact extension of a closed solvable normal subgroup, in particular, is amenable, (2) has finite one-moment or (3) has density and in case the characteristic of is positive, the radical of is -defined. We also discuss the spectral radius of the convolution operator of a probability measure on a locally compact group , we show that it is always positive for any probability measure on , and it is also multiplicative in case of symmetric commuting measures.
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We develop for a large class of locally compact groups a method of approximation of convolution operators on by finitely supported measures with control of the support and of the operator norm of the approximating measures.
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Let A be an expansive dilation. We define weakly strongly singular integral kernels and study the action of the operators induced by these kernels on anisotropic Hardy spaces associated with A. 相似文献