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Sharp Hardy’s inequality for Jacobi and symmetrized Jacobi trigonometric expansions
Journal of Approximation Theory ( IF 0.9 ) Pub Date : 2020-04-23 , DOI: 10.1016/j.jat.2020.105422
Paweł Plewa

Four Jacobi settings are considered in the context of Hardy’s inequality: the trigonometric polynomials and functions, and the corresponding symmetrized systems. In the polynomial cases sharp Hardy’s inequality is proved for the type parameters α,β(1,)d, whereas in the function systems for α,β[12,)d. The ranges of these parameters are the widest in which the corresponding orthonormal bases are composed of bounded functions. Moreover, the sharp L1-analogues of Hardy’s inequality are obtained with the same restrictions on the parameters α and β.



中文翻译:

Sharp Hardy对于Jacobi和对称Jacobi三角展开式的不等式

在Hardy不等式的上下文中考虑了四个Jacobi设置:三角多项式和函数,以及相应的对称系统。在多项式情况下,针对类型参数证明了尖锐的Hardy不等式αβ-1个d,而在功能系统中 αβ[-1个2d。这些参数的范围是最宽的,其中相应的正交基数由有界函数组成。而且,犀利大号1个-在参数相同的限制下获得哈代不等式的模拟 αβ

更新日期:2020-04-23
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