共查询到20条相似文献,搜索用时 78 毫秒
1.
In this paper we investigate the convolution Hankel transforms on the Zemanian spaces of Hankel transformable functions and distributions. The convolution Hankel transform is defined on generalized functions by using the adjoint method. Our new definition includes as special cases other known definitions of the convolution Hankel transform of distributions. Finally we establish a distributional inversion formula for the transformation under consideration involving Bessel differential operators. 相似文献
2.
The topologies of simple convergence and of bounded convergence are shown to coincide on the spaces of Hankel multipliers
and of Hankel convolution operators. The properties of these spaces being bornological, nuclear, Montel, and reflexive are
established. 相似文献
3.
F. Chouchene H. Mejjaoli M. Mili K. Trimèche 《Mediterranean Journal of Mathematics》2014,11(2):577-600
In this paper, we study the Jacobi–Dunkl convolution operators on some distribution spaces. We characterize the Jacobi–Dunkl convolution operators as those ones that commute with the Jacobi–Dunkl translations and with the Jacobi–Dunkl operators. Also we prove that the Jacobi–Dunkl convolution operators are hypercyclic and chaotic on the spaces under consideration and we give a universality property for the generalized heat equation associated with them. 相似文献
4.
N. Popa 《Complex Analysis and Operator Theory》2017,11(8):1765-1780
In this paper we consider some Banach spaces of analytic functions on the unit disk generated by the cone of analytic functions with monotone decreasing Taylor coefficients. We get that some of these spaces are Banach lattices with respect to this cone. Different ordered spaces of linear bounded operators acting between the previous spaces are also investigated, with emphasis on the so-called regular multipliers and Hankel operators. 相似文献
5.
M. A. Zakaryan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2013,48(5):221-232
The paper considers weighted spaces of harmonic functions. Having lower and upper bounds for the equivalent kernels of such spaces we consider Toeplitz and Hankel operators with different symbols. The Fredholm criterion for these operators on some compact is also studied. 相似文献
6.
Aline Bonami Sandrine Grellier Mohammad Kacim 《Transactions of the American Mathematical Society》2008,360(3):1377-1390
We extend to multilinear Hankel operators the fact that some truncations of bounded Hankel operators are still bounded. We prove and use a continuity property of bilinear Hilbert transforms on products of Lipschitz spaces and Hardy spaces.
7.
In this paper we consider a class of weighted integral operators onL
2 (0, ) and show that they are unitarily equivalent to Hankel operators on weighted Bergman spaces of the right half plane. We discuss conditions for the Hankel integral operator to be finite rank, Hilbert-Schmidt, nuclear and compact, expressed in terms of the kernel of the integral operator. For a particular class of weights these operators are shown to be unitarily equivalent to little Hankel operators on weighted Bergman spaces of the disc, and the symbol correspondence is given. Finally the special case of the unweighted Bergman space is considered and for this case, motivated by approximation problems in systems theory, some asymptotic results on the singular values of Hankel integral operators are provided. 相似文献
8.
Jorge J. Betancor 《Rendiconti del Circolo Matematico di Palermo》1999,48(1):51-64
In this paper we characterize weak type (1,1) inequalities for Hankel convolution operators by means of discrete methods.
Partially supported by DGICYT Grant PB 94-0591 (Spain). 相似文献
9.
西方给出了C^n中单位球上的带权的Bergman空间上具一般符号的Toeplitz算子和Hankel算子为紧的充要条件。 相似文献
10.
In the paper, we give characterizations of Hankel operators on generalizedH
2 spaces and obtain some properties for corresponding Hankel algebras.Supported in part by NSF of China 相似文献
11.
本文讨论了Dirichlet型空间上的再生核,并对Dirichlet型空间上乘法算子,Hankel算子和小Hankel算子的基本性质进行了研究,同时也给出了这些算子的有界性,紧性和Schatten理想的初步刻画。 相似文献
12.
Zen Harper 《Journal of Evolution Equations》2005,5(3):387-405
We study convolution operators on weighted Lebesgue spaces and obtain weight characterisations for boundedness of these operators
with certain kernels. Our main result is Theorem 3 which enables us to obtain results for certain kernel functions supported
on bounded intervals; in particular we get a direct proof of the known characterisations for Steklov operators in Section
3 by using the weighted Hardy inequality. Our methods also enable us to obtain new results for other kernel functions in Section
4. In Section 5 we demonstrate that these convolution operators are related to operators arising from the Weiss Conjecture
(for scalar-valued observation functionals) in linear systems theory, so that results on convolution operators provide elementary examples of nearly bounded semigroups
not satisfying the Weiss Conjecture. Also we apply results on the Weiss Conjecture for contraction semigroups to obtain boundedness
results for certain convolution operators. 相似文献
13.
14.
Carme Cascante Joan Fàbrega Joaquín M. Ortega 《Integral Equations and Operator Theory》2010,66(4):495-528
We compute the norm of pointwise multiplication operators, Toeplitz and Big Hankel operators with antiholomorphic symbols,
defined on Besov spaces. These norms will be given in terms of Carleson measures for Besov spaces related to the symbol. 相似文献
15.
Zhijian Wu 《Integral Equations and Operator Theory》1996,24(3):352-371
We study the commutator of the multiplication and harmonic Bergman projection, Hankel and Toeplitz operators on the harmonic Bergman spaces. The same type operators have been well studied on the analytic Bergman spaces. The main difficulty of this study is that the bounded harmonic function space is not an algebra! In this paper, we characterize theL
p boundedness and compactness of these operators with harmonic symbols. Results about operators in Schatten classes, the cut-off phenomenon and general symbols are also included.Partially supported by a grant from the Research Grants Committee of the University of Alabama. 相似文献
16.
We study convolution operators in Bessel potential spaces and (fractional) Sobolev spaces over a finite interval. The main purpose of the investigation is to find conditions on the convolution kernel or on a Fourier symbol of these operators under which the solutions inherit higher regularity from the data. We provide conditions which ensure the transmission property for the finite interval convolution operators between Bessel potential spaces and Sobolev spaces. These conditions lead to smoothness preserving properties of operators defined in the above-mentioned spaces where the kernel, cokernel and, therefore, indices do not depend on the order of differentiability. In the case of invertibility of the finite interval convolution operator, a representation of its inverse is presented in terms of the canonical factorization of a related Fourier symbol matrix function. 相似文献
17.
On the Sobolev boundedness results of the product of pseudo-differential operators involving a couple of fractional Hankel transforms 下载免费PDF全文
This article is concerned with the study of pseudo-differential operators associated with fractional Hankel transform. The product of two fractional pseudo-differential operators is defined and investigated its basic properties on some function space. It is shown that the pseudo-differential operators and their products are bounded in Sobolev type spaces. Particular cases are discussed. 相似文献
18.
Hankel operators with anti-holomorphic symbols are studied for a large class of weighted Fock spaces on ? n . The weights defining these Hilbert spaces are radial and subject to a mild smoothness condition. In addition, it is assumed that the weights decay at least as fast as the classical Gaussian weight. The main result of the paper says that a Hankel operator on such a Fock space is bounded if and only if the symbol belongs to a certain BMOA space, defined via the Berezin transform. The latter space coincides with a corresponding Bloch space which is defined by means of the Bergman metric. This characterization of boundedness relies on certain precise estimates for the Bergman kernel and the Bergman metric. Characterizations of compact Hankel operators and Schatten class Hankel operators are also given. In the latter case, results on Carleson measures and Toeplitz operators along with Hörmander’s L 2 estimates for the $\bar{\partial}$ operator are key ingredients in the proof. 相似文献
19.
Lova Zakariasy 《Proceedings of the American Mathematical Society》2003,131(4):1177-1180
We show that on the harmonic Bergman spaces, the Hankel operators with nonconstant harmonic symbol cannot be of finite rank.
20.
Lu YU-FENG YANG JUN 《东北数学》2009,25(2):159-164
In this paper we concern with the characterization of bounded linear operators S acting on the weighted Bergman spaces on the unit ball. It is shown that, if S satisfies the commutation relation STzi = Tzi(i =1,..,n), where Tzi = zif and Tzi= P(zif) where P is the weighted Bergman projection, then S must be a Hankel operator. 相似文献