共查询到20条相似文献,搜索用时 15 毫秒
1.
Karlheinz Grö chenig Michael Leinert 《Journal of the American Mathematical Society》2004,17(1):1-18
We prove non-commutative versions of Wiener's Lemma on absolutely convergent Fourier series (a) for the case of twisted convolution and (b) for rotation algebras. As an application we solve some open problems about Gabor frames, among them the problem of Feichtinger and Janssen that is known in the literature as the ``irrational case'.
2.
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
3.
Nguyen Xuan Thao Hoang Thi Van Anh 《Mathematical Methods in the Applied Sciences》2014,37(15):2308-2319
In this paper, we construct and study a new generalized convolution (f * g)(x) of functions f,g for the Hartley (H1,H2) and the Fourier sine (Fs) integral transforms. We will show that these generalized convolutions satisfy the following factorization equalities: We prove the existence of this generalized convolution on different function spaces, such as . As examples, applications to solve a type of integral equations and a type of systems of integral equations are presented. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
4.
R. A. Bandaliev 《Mathematical Notes》2006,80(1-2):3-10
In this paper, we prove a theorem on the boundedness of a convolution operator in a weighted Lebesgue space with kernel satisfying a certain version of Hörmander’s condition. 相似文献
5.
It was well known that Calderón-Zygmund operators T are bounded on Hp for provided T∗(1)=0. A new Hardy space , where b is a para-accretive function, was introduced in [Y. Han, M. Lee, C. Lin, Hardy spaces and the Tb-theorem, J. Geom. Anal. 14 (2004) 291-318] and the authors proved that Calderón-Zygmund operators T are bounded from the classical Hardy space Hp to the new Hardy space if T∗(b)=0. In this note, we give a simple and direct proof of the boundedness of Calderón-Zygmund operators via the vector-valued singular integral operator theory. 相似文献
6.
We study convolution type operators with kernels that have Fourier transforms in the class of piecewise continuous matrix functions. These convolution operators are assumed to act between Sobolev spaces defined on a union of a finite and a semi-infinite intervel. The main result is a criterion for the Fredholm property of these operators. An application to a problem related to diffraction theory is illustrated. 相似文献
7.
Daniel Oberlin Hart F. Smith 《Proceedings of the American Mathematical Society》1999,127(10):2911-2915
We obtain nearly sharp estimates for the norms of certain convolution operators.
8.
The boundedness of maximal multilinear commutator on certain weighted spaces is obtained. The boundedness of mulitilinear commutators of singular integrals with Calderon-Zygmund kernel on Herz-type spaces is also considered. 相似文献
9.
In this paper, we prove the Lp (?n ) boundedness for higher commutators of singular integrals with rough kernels belonging to certain block spaces provided that 1 < p < ∞ (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
10.
S. A. Buterin 《Mathematical Notes》2006,80(5-6):631-644
We consider a one-dimensional perturbation of the convolution operator. We study the inverse reconstruction problem for the convolution component using the characteristic numbers under the assumption that the perturbation summand is known a priori. The problem is reduced to the solution of the so-called basic nonlinear integral equation with singularity. We prove the global solvability of this nonlinear equation. On the basis of these results, we prove a uniqueness theorem and obtain necessary and sufficient conditions for the solvability of the inverse problem. 相似文献
11.
Yong Ding Shanzhen Lu Dachun Yang 《Proceedings of the American Mathematical Society》2001,129(4):1127-1136
In this paper the authors give a criterion on the weighted boundedness of the multilinear oscillatory singular integral operators with rough kernels.
12.
In this paper, we extend Hu and Zhang’s results in [2] to different case. 相似文献
13.
Luis P. Castro Rita C. Guerra Nguyen Minh Tuan 《Mathematical Methods in the Applied Sciences》2020,43(7):4835-4846
We propose four new convolutions exhibiting convenient factorization properties associated with two finite interval integral transformations of Fourier-type together with their norm inequalities. Moreover, we study the solvability of a class of integral equations of Wiener-Hopf plus Hankel type (on finite intervals) with the help of the factorization identities of such convolutions. Fourier-type series are used to produce the solution formula of such equations, and a Shannon-type sampling formula is also obtained. 相似文献
14.
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
15.
In this paper some Voronovskaya approximation formulae for a class of Mellin convolution operators of the type (Tw f)(x,y) = ∫R2+ Kw(tx-1,vy-1)f(t,v)tvdtdv are given. Moreover, various examples are discussed. 相似文献
16.
Jizheng Huang 《Bulletin des Sciences Mathématiques》2009,133(6):588-596
In this paper, we will consider the boundedness of Weyl multiplier on Hardy spaces associated with twisted convolution. In order to get our result, we need to give some characterizations of the Hardy space associated with twisted convolution. Including Lusin area integral, Littlewood-Paley g-function. 相似文献
17.
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
18.
Pingrun Li 《Mathematical Methods in the Applied Sciences》2019,42(8):2631-2645
In this paper, we first establish a locality theory for the Noethericity of generalized boundary value problems on the spaces . By means of this theory, of the classical boundary value theory, and of the theory of Fourier analysis, we discuss the necessary and sufficient conditions of the solvability and obtain the general solutions and the Noether conditions for one class of generalized boundary value problems. All cases as regards the index of the coefficients in the equations are considered in detail. Moreover, we apply our theoretical results to the solvability of singular integral equations with variable coefficients. Thus, this paper will be of great significance for the study of improving and developing complex analysis, integral equation, and boundary value theory. 相似文献
19.
20.
Kh. A. Khachatryan M. G. Kostanyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2008,43(3):145-156
The paper investigates a class of convolution type integro-differential equations for vector-functions. Some special factorization methods are used to prove the solvability in several functional spaces. 相似文献