共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we characterize when the Toeplitz operator Tf and the Hankel operator Hg commute on the Hardy space of the bidisk. For certain types of bounded symbols f and g, we give a necessary and sufficient condition on the symbols to guarantee TfHg = HgTf. 相似文献
2.
This paper deals with an operator theory of compressed shifts on the Hardy space over the bidisk. We give commutant lifting
type theorems and some interpolation theorems in two variables. 相似文献
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Yong DING Shan Zhen LU Qing Ying XUE 《数学学报(英文版)》2007,23(9):1537-1552
In this paper, the authors prove that if Ω satisfies a class of the integral Dini condition, then the parametrized area integral μΩ,S^ρ is a bounded operator from the Hardy space H1 (R^n) to L1 (R^n) and from the weak Hardy space H^1,∞ (R^n) to L^1,∞ (R^n), respectively. As corollaries of the above results, it is shown that μΩ,S^ρ is also an operator of weak type These conclusions are substantial improvement and (1, 1) and of type (p,p) for 1 〈 p 〈 2, respectively extension of some known results. 相似文献
4.
Paula Cerejeiras Uwe Kähler Min Ku Frank Sommen 《Journal of Fourier Analysis and Applications》2014,20(4):715-750
We study the boundary behavior of discrete monogenic functions, i.e. null-solutions of a discrete Dirac operator, in the upper and lower half space. Calculating the Fourier symbol of the boundary operator we construct the corresponding discrete Hilbert transforms, the projection operators arising from them, and discuss the notion of discrete Hardy spaces. Hereby, we focus on the 3D-case with the generalization to the n-dimensional case being straightforward. 相似文献
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We consider properties related to weighted composition operators boundedly acting from the classical Hardy space H p to H q for \({1 \leq q < p < \infty}\) . Especially, we shall completely determine path connected components in the set of weighted composition operators and explicitly characterize by function-theoretic properties of analytic self-maps. 相似文献
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We investigate the accuracy of certain sufficient conditions for multipliers of power series in Hardy spaces. 相似文献
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In this paper we introduce and study the anisotropic local Hardy spaces
hAp(\mathbbRn)h_{A}^{p}(\mathbb{R}^{n}) 0<p≤1, associated with the expansive matrix A. We obtain an atomic characterization of the distributions in
hAp(\mathbbRn)h_{A}^{p}(\mathbb{R}^{n}). Also we describe the dual spaces of our local Hardy anisotropic spaces as anisotropic Campanato type spaces. 相似文献
11.
We introduce and explore Hardy spaces defined by mixed Lebesgue norms and anisotropic dilations. We prove that the definitions of these spaces in terms of smooth, non-tangential, auxiliary, grand, and Poisson maximal operators coincide. We also study the relation between anisotropic mixed-norm Hardy spaces and mixed-norm Lebesgue spaces. 相似文献
12.
设G为局部域K上的2n+1维Heisenberg群.本文证明了通过各种极大函数定义的Hardy空间的等价性,给出了Hardy空间的原子分解.利用这些等价定义及一些卷积算子定理,给出了Hardy空间的平方函数刻画——Luzin面积函数刻画与Litlewood-Paley平方函数刻画 相似文献
13.
Bebe Prunaru 《Integral Equations and Operator Theory》2008,61(1):121-145
In this paper we establish a connection between the approximate factorization property appearing in the theory of dual algebras
and the spectral inclusion property for a class of Toeplitz operators on Hilbert spaces of vector valued square integrable
functions. As an application, it follows that a wide range of dual algebras of subnormal Toeplitz operators on various Hardy
spaces associated to function algebras have property (A
1(1)). It is also proved that the dual algebra generated by a spherical isometry (with a possibly infinite number of components)
has the same property. One particular application is given to the existence of unimodular functions sitting in cyclic invariant
subspaces of weak* Dirichlet algebras. Moreover, by this method we provide a unified approach to several Toeplitz spectral
inclusion theorems.
Research partially supported by grant CNCSIS GR202/2006 (cod 813). 相似文献
14.
《复变函数与椭圆型方程》2012,57(5):373-382
A monster in the sense of Luh is a holomorphic function on a simply connected domain in the complex plane such that it and all its derivatives and antiderivatives exhibit an extremely wild behaviour near the boundary. In this paper, the Hardy spaces H p and the Bergman spaces B p (1 h p < X ) on the unit disk are considered, and it is shown that there are no Luh-monsters in them. Nevertheless, it is proved that T -monsters (as introduced by the authors in an earlier work) can be found in each of these spaces for any finite order linear differential operator T . 相似文献
15.
V. V. Kapustin 《Journal of Mathematical Sciences》2002,110(5):2986-2990
We study the following problem: to describe weights w on the unit circle such that the analytic and antianalytic subspaces of the corresponding weighted space
Lp(w)
have nonzero intersection. In the special case p=2, the problem is equivalent to the well-known problem on exposed points in H
1. We show that the property in question is local, i.e., it depends on local behavior of the weight w at each point of the unit circle. Some necessary and sufficient conditions in terms of the Herglotz integrals are obtained. Bibliography: 6 titles. 相似文献
16.
Sándor Z. Németh 《Positivity》2006,10(2):299-314
Computational formulae for scalar derivatives of mappings and pairs of mappings in the direction of a set will be given. These
formulae are very important for explicitly verifying conditions of existence for fixed point theorems, surjectivity theorems,
integral equations, variational inequalities and complementarity problems under additional differentiability conditions. To
emphasize this idea at the end of the paper we give an application to complementarity problems. Some theorems which extend
the correspondence between monotone mappings and scalar derivatives from Euclidean spaces to Hilbert spaces will also be given. 相似文献
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利用Hardy空间中函数的高阶导数的估计,通过构造一些新的检验函数,运用解析函数的性质与算子理论,给出了从Hardy空间到Zygmund型空间的Riemann—Stieltjes算子的有界性和紧性的特征,获得了若干个充要条件. 相似文献
20.
In this article we provide several generalizations of inequalities bounding the commutator of two linear operators acting on a Hilbert space which relate to the Heisenberg uncertainty principle and time/frequency analysis of periodic functions. We develop conditions that ensure these inequalities are sharp and apply our results to concrete examples of importance in the literature. 相似文献