共查询到20条相似文献,搜索用时 46 毫秒
1.
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
2.
We construct a calculus for generalized SG Fourier integral operators, extending known results to a broader class of symbols of SG type. In particular, we do not require that the phase functions are homogeneous. An essential ingredient in the proofs is a general criterion for asymptotic expansions within the Weyl-Hörmander calculus. We also prove the L2(Rd)-boundedness of the generalized SG Fourier integral operators having regular phase functions and amplitudes uniformly bounded on R2d. 相似文献
3.
V. M. Deundyak 《Mathematical Notes》2010,87(5-6):672-686
In the space L p (? n ), 1 < p < +∞, we consider a new class of integral operators with kernels homogeneous of degree ?n, which includes the class of operators with homogeneous SO(n)-invariant kernels; we study the Banach algebra generated by such operators with multiplicatively weakly oscillating coefficients. For operators from this algebra, we define a symbol in terms of which we formulate a Fredholm property criterion and derive a formula for calculating the index. An important stage in obtaining these results is the establishment of the relationship between the operators of the class under study and the operators of one-dimensional convolution with weakly oscillating compact coefficients. 相似文献
4.
5.
In this paper we develop elements of the global calculus of Fourier integral operators in ${{\mathbb R}^n}$ under minimal decay assumptions on phases and amplitudes. We also establish global weighted Sobolev L2 estimates for a class of Fourier integral operators that appears in the analysis of global smoothing problems for dispersive partial differential equations. As an application, we exhibit a new type of weighted estimates for hyperbolic equations, where the decay of data in space is quantitatively translated into the time decay of solutions. 相似文献
6.
In this paper we consider L2 bounds and weak type (1.1) bounds for a class of singular integral operators introduced by R. Fefferman and Namazi. Then,
we solve two problems proposed by Shi. 相似文献
7.
Chen Wenzhong 《分析论及其应用》1989,5(2):9-24
In 1984, L. C. Hsu, X. J. Yang and the auther[1] defined a class of summation-integral operators. Later, the author[2]–[5], Mazhar-Totik[6] and Sahai-Prased[7] studied some specific exponential type integral operators, separately. The purpose of this paper is to introduce and study
some more general mixed exponential type integral operators. 相似文献
8.
Chunjie Zhang 《分析论及其应用》2011,27(3):278-287
In this paper, we consider a class of Banach space valued singular integrals. The Lp boundedness of these operators has already been obtained. We shall discuss their boundedness from BMO to BMO. As applications, we get BMO boundednessfor the classic g-function and the Marcinkiewicz integral. Some known results are improved. 相似文献
9.
The main aim of the paper is Fredholm properties of a class of bounded linear operators acting on weighted Lebesgue spaces
on an infinite metric graph Γ which is periodic with respect to the action of the group
\mathbb Zn{{\mathbb {Z}}^n} . The operators under consideration are distinguished by their local behavior: they act as (Fourier) pseudodifferential operators
in the class OPS
0 on every open edge of the graph, and they can be represented as a matrix Mellin pseudodifferential operator on a neighborhood
of every vertex of Γ. We apply these results to study the Fredholm property of a class of singular integral operators and
of certain locally compact operators on graphs. 相似文献
10.
In the space L p (? n ), 1 < p < ??, we study a new wide class of integral operators with anisotropically homogeneous kernels. We obtain sufficient conditions for the boundedness of operators from this class. We consider the Banach algebra generated by operators with anisotropically homogeneous kernels of compact type and multiplicatively slowly oscillating coefficients. We establish a relationship between this algebra and multidimensional convolution operators, and construct a symbolic calculus for it. We also obtain necessary and sufficient conditions for the Fredholm property of operators from this algebra. 相似文献
11.
In this paper we develop a method for the approximation of a broad class of operator equations by reproducing kernels. The relevant operators are defined on Hilbert spaces. Necessary and sufficient conditions for the convergence of the approximation are discussed in detail. The results can be applied-for example-to Fredholm integral operators of the first and second kind and to ordinary and partial differential operators of elliptic type. In this context we refer to [9] for methods to construct reproducing kernels. 相似文献
12.
Ahmad Al-Salman 《Journal of Mathematical Analysis and Applications》2004,299(1):72-88
In this paper, we study a classes of oscillatory singular integral operators of nonconvolution type with phases more general than polynomials. We prove that such operators are bounded on Lp provided their kernels satisfy a very weak condition. In addition, we also study the related truncated oscillatory singular integral operators. Moreover, we present a class of unbounded oscillatory singular integral operators. 相似文献
13.
15.
Brian Jefferies 《Integral Equations and Operator Theory》2016,84(3):419-428
A necessary and sufficient condition is given for a positive bounded linear operator with an integral kernel to be trace class on L2(μ) for a σ-finite measure μ. The condition refines earlier criteria for positive Hilbert–Schmidt operators and positive integral operators with continuous kernels on a locally compact space. 相似文献
16.
We consider the C*-algebra generated by multidimensional integral operators with (?n)th-order homogeneous kernels and by the operators of multiplication by oscillating coefficients of the form |x|iα. For this algebra, we construct an operator symbolic calculus and obtain necessary and sufficient conditions for the Fredholm property of an operator in terms of this calculus. 相似文献
17.
We obtain estimates and convergence results with respect to ?-variation in spaces BVΦ for a class of linear integral operators whose kernels satisfy a general homogeneity condition. Rates of approximation are also obtained. As applications, we apply our general theory to the case of Mellin convolution operators, to that one of moment operators and finally to a class of operators of fractional order. 相似文献
18.
Jorge J. Betancor Juan C. Fariña Lourdes Rodríguez-Mesa Ricardo Testoni 《Integral Equations and Operator Theory》2011,70(4):511-539
In this paper we represent the kth Riesz transform in the ultraspherical setting as a principal value integral operator for every \({k \in \mathbb N}\). We also measure the speed of convergence of the limit by proving L p -boundedness properties for the oscillation and variation operators associated with the corresponding truncated operators. 相似文献
19.
Huo Xiong WU Shan Zhi YANG 《数学学报(英文版)》2008,24(2):177-184
This paper is devoted to the study of a class of singular integral operators defined by polynomial mappings on product domains. Some rather weak size conditions, which imply the Lp boundedness of these singular integral operators as well as the corresponding maximal truncated singular integral operators for some fixed 1〈p〈 ∞,are given. 相似文献
20.
In this paper, we study the approximation of identity operator and the convolution integral operator Bm by Fourier partial sum operators, Fejr operators, Valle-Poussin operators, Cesárooperators and Abel mean operators, respectively, on the periodic Wiener space (C1(R),Wo) and obtainthe average error estimations. 相似文献