排序方式: 共有5条查询结果,搜索用时 15 毫秒
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Qiulan Qi & Juan Liu 《数学研究通讯:英文版》2012,28(1):1-9
In this paper we give a strong converse inequality of type B in terms of
unified $K$-functional $K^α_λ (f, t^2) (0 ≤ λ ≤ 1, 0 < α < 2)$ for the Meyer-König and
Zeller-Durrmeyer type operators. 相似文献
2.
Walter Trebels 《Proceedings of the American Mathematical Society》1999,127(10):2883-2887
Within the setting of abstract Cesàro-bounded Fourier series a -functional is introduced and characterized by the convergence behavior of some linear means. Applications are given within the framework of Jacobi, Laguerre and Hermite expansions. In particular, Ditzian's (1996) equivalence result in the setting of Legendre expansions is covered.
3.
Sergei V. Astashkin Lech Maligranda 《Proceedings of the American Mathematical Society》2004,132(10):2929-2938
We show that if is a rearrangement invariant space on that is an interpolation space between and and for which we have only a one-sided estimate of the Boyd index 1/p, 1 < p < \infty$">, then is an interpolation space between and . This gives a positive answer for a question posed by Semenov. We also present the one-sided interpolation theorem about operators of strong type and weak type .
4.
The generalized summation integral type operators with Beta basis functions are widely studied. At present, the investigations for the properties of these operators are only limited to the functions of bounded variation. Some authors studied the rate of point-wise rate of convergence, asymptotic formula of Voronovskaja type, and some direct results about these type of operators. The present paper considers the direct, inverse and equivalence theorems of modified summation integral type operators in the Lp spaces. 相似文献
5.
Alexei Yu. Karlovich Lech Maligranda 《Proceedings of the American Mathematical Society》2001,129(9):2727-2739
In this paper we deal with the interpolation from Lebesgue spaces and , into an Orlicz space , where and for some concave function , with special attention to the interpolation constant . For a bounded linear operator in and , we prove modular inequalities, which allow us to get the estimate for both the Orlicz norm and the Luxemburg norm,
where the interpolation constant depends only on and . We give estimates for , which imply . Moreover, if either or , then . If , then , and, in particular, for the case this gives the classical Orlicz interpolation theorem with the constant .
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