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101.
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 .
102.
Let
be a unit sphere of the d–dimensional Euclidean space ℝ
d
and let
(0 < p ≤ 1) denote the real Hardy space on
For 0 < p ≤ 1 and
let
E
j
(f,H
p
) (j = 0, 1, ...) be the best approximation of f by spherical polynomials of degree less than or
equal to j, in the space
Given a distribution f on
its Cesàro mean of order δ > –1 is
denoted by
For 0 < p ≤ 1, it is known that
is the critical index for the uniform
summability of
in the metric H
p
. In this paper, the following result is proved:
Theorem
Let
0<p<1 and
Then for
where
A
N
(f)≈B
N
(f) means that there’s a positive constant C, independent of N and f, such that
In the case
d = 2, this result was proved by Belinskii in 1996.
The authors are partially supported by NNSF of China under the grant # 10071007 相似文献
103.
Yuan Xu 《Proceedings of the American Mathematical Society》1998,126(10):3027-3036
We study the Fourier expansion of a function in orthogonal polynomial series with respect to the weight functions
on the standard simplex in . It is proved that such an expansion is uniformly summable on the simplex for any continuous function if and only if . Moreover, it is shown that means define a positive linear polynomial identity, and the index is sharp in the sense that means are not positive for .
104.
105.
We characterize weak compactness and weak conditional compactness of subsets of in terms of regular methods of summability. We also study when these results still hold using only convergence in the sense of Cesàro.
106.
We introduce the p-adic weighted multilinear Hardy-Cesàro operator. We also obtain the necessary and sufficient conditions on weight functions to ensure the boundedness of that operator on the product of Lebesgue spaces, Morrey spaces, and central bounded mean oscillation spaces. In each case, we obtain the corresponding operator norms. We also characterize the good weights for the boundedness of the commutator of weighted multilinear Hardy-Cesàro operator on the product of central Morrey spaces with symbols in central bounded mean oscillation spaces. 相似文献
107.
本文以螯合阳离子、螯合阴离子和具有阴、阳电性互变异构体的三种类型的显色体系为例 ,比较研究了未经修饰的 β -环糊精 (β-CD)与经荷阴离子、阳离子取代基修饰的 β-CD衍生物对这三种类型显色体系的增效作用的机理 ,总结出这些衍生物对显色反应作用的规律 . 相似文献
108.
S. A. Stepanyants 《Mathematical Notes》1999,65(1):99-108
In this paper, we study gap conditions ensuring, for the class of series satisfying them, that the Cesàro methods (C, k) and (C, α) with fixedk and α (0<k<α) are equivalent. We obtain a sufficient condition in which gaps of the corresponding sizes separate uniformly bounded sets
ofk+1 nonzero elements rather than neighboring nonzero elements (as in the classical case ofk=0).
Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 118–129, January, 1999. 相似文献
109.
利用泛函分析以及多复变方法,研究了多圆柱上加权Bergman空间到Bloch型空间的加权Cesàro算子问题,得到了多圆柱上加权Bergman空间到Bloch型空间的加权Cesàro算子为有界算子和紧算子的充要条件,并给出了单位圆盘上加权Bergman空间到Bloch型空间的加权Cesàro算子为有界算子和紧算子的充要条件。 相似文献
110.
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