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1.
Jacques Delaporte Antoine Derighetti 《Proceedings of the American Mathematical Society》1996,124(4):1159-1169
We compute the best bound for the approximate units of the augmentation ideal of the group algebra of a locally compact amenable group . More generally such a calculation is performed for the kernel of the canonical map from onto , being a closed amenable subgroup of . Analogous results involving certain ideals of the Fourier algebra of an amenable group are also discussed.
2.
Jie Xiao 《Proceedings of the American Mathematical Society》1997,125(12):3613-3616
In this note, we show that Cesàro transforms of Fourier cosine or sine coefficients of any -function are Fourier cosine or sine coefficients of some -function.
3.
Tianxuan Miao 《Proceedings of the American Mathematical Society》2004,132(12):3671-3678
For a locally compact group and , let be the Figà-Talamanca-Herz algebra and let be its dual Banach space. For a Banach -module of , we denote the norm closure of the subspace of the elements in with compact support by . We prove that an element of is in if and only if for any 0$">, there exists a compact subset of such that for all with and . In particular, we have that an element of is in if and only if for any 0$">, there exists a compact subset of such that for all with . If has an orthogonal complement in , we characterize by the following condition: is in if and only if for any 0$"> and any compact subset of , there exists some with and such that \Vert u\Vert - \epsilon $">. Some results of Flory (1971) and Miao (1999) can be obtained from our main theorems by taking and as some -subalgebras of .
4.
Zhangjian Hu 《Proceedings of the American Mathematical Society》2003,131(7):2171-2179
We define an extended Cesàro operator with holomorphic symbol in the unit ball of as
where is the radial derivative of . In this paper we characterize those for which is bounded (or compact) on the mixed norm space .
where is the radial derivative of . In this paper we characterize those for which is bounded (or compact) on the mixed norm space .
5.
6.
Bilinear operators on Herz-type Hardy spaces 总被引:4,自引:0,他引:4
Loukas Grafakos Xinwei Li Dachun Yang 《Transactions of the American Mathematical Society》1998,350(3):1249-1275
The authors prove that bilinear operators given by finite sums of products of Calderón-Zygmund operators on are bounded from into if and only if they have vanishing moments up to a certain order dictated by the target space. Here are homogeneous Herz-type Hardy spaces with and . As an application they obtain that the commutator of a Calderón-Zygmund operator with a BMO function maps a Herz space into itself.
7.
Let be Banach spaces and let be closed operator ideals. Let be a Banach space having the Radon-Nikodým property. The main results are as follows. If is a Hahn-Banach extension operator, then there exists a set of Hahn-Banach extension operators , , such that , where . If is an ideal in for all equivalently renormed versions of , then there exist Hahn-Banach extension operators and such that .
8.
In this note, the boundedness of the Cesàro operator on mixed norm space , , is proved.
9.
We provide an alternative proof to those by Shkarin and by Bayart and Matheron that the operator D of complex differentiation supports a hypercyclic algebra on the space of entire functions. In particular we obtain hypercyclic algebras for many convolution operators not induced by polynomials, such as , , or , where . In contrast, weighted composition operators on function algebras of analytic functions on a plane domain fail to support supercyclic algebras. 相似文献
10.
In this paper we study the Hankel convolution operators on the space of even and entire functions and on Schwartz distribution spaces. We characterize the Hankel convolution operators as those ones that commute with Hankel translations and with a Bessel operator. Also we prove that the Hankel convolution operators are hypercyclic and chaotic on the spaces under consideration. 相似文献
11.
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
12.
Let μ, v ∈ [0, 1) be normal functions and g be holomorphic function on the unit ball. In this paper, we prove that the generalized Cesaro operator Tg :βμ→βv is bounded and compact. 相似文献
13.
本文研究了一类复合型幂级数展开式,证明了一个收敛性定理并举例说明其应用.在注记中指出了可进一步研究的问题. 相似文献
14.
Luis A. Caffarelli Cristian E. Gutié rrez 《Transactions of the American Mathematical Society》1996,348(3):1075-1092
In this paper we consider a family of convex sets in , , , , satisfying certain axioms of affine invariance, and a Borel measure satisfying a doubling condition with respect to the family The axioms are modelled on the properties of the solutions of the real Monge-Ampère equation. The purpose of the paper is to show a variant of the Calderón-Zygmund decomposition in terms of the members of This is achieved by showing first a Besicovitch-type covering lemma for the family and then using the doubling property of the measure The decomposition is motivated by the study of the properties of the linearized Monge-Ampère equation. We show certain applications to maximal functions, and we prove a John and Nirenberg-type inequality for functions with bounded mean oscillation with respect to
15.
Elijah Liflyand Ferenc Mó ricz 《Proceedings of the American Mathematical Society》2000,128(5):1391-1396
We prove that the Hausdorff operator generated by a function is bounded on the real Hardy space . The proof is based on the closed graph theorem and on the fact that if a function in is such that its Fourier transform equals for (or for ), then .
16.
In this article, applying the result of complete convergence for negatively associated (NA) random variables which is obtained by Chen et al.\ucite{14}, the equivalent conditions of complete convergence for weighted sums of arrays of row-wise negatively associated random variables is investigated. As a result, the corresponding results of Liang\ucite{11} is generalized, moreover, the proof procedure is simplified greatly which is different from truncation method of Liang's. Thus, Gut's\ucite{13} result on Ces\`{a}ro summation of i.i.d. random variables is extended. 相似文献
17.
Pham Hoang Hiep 《Proceedings of the American Mathematical Society》2008,136(6):2007-2018
The main aim of the present note is to study the convergence in on a compact Kahler mainfold . The obtained results are used to study global extremal functions and describe the -pluripolar hull of an -pluripolar subset in .
18.
Recently some classical operator quasi-interpolants were introduced to obtain much faster convergence. A.T. Diallo investigated some approximation properties of Szasz-Mirakjan Quasi-Interpolants, but he obtained only direct theorem with Ditzian-Totik modulus wφ^2r (f, t). In this paper, we extend Diallo's result and solve completely the characterization on the rate of approximation by the method of quasi-interpolants to functions f ∈ CB[0, ∞) by making use of the unified modulus wφ^2r(f, t) (0≤λ≤ 1). 相似文献
19.
For a linear autonomous difference equation with a unique real eigenvalue , it is shown that for every solution the ratio of and the eigensolution corresponding to is Cesàro summable to a limit which can be expressed in terms of the initial data. As a consequence, for most solutions the Lyapunov characteristic exponent is equal to . The proof is based on a Tauberian theorem for the Laplace transform.