Mutual estimates of Lp-norms and the Bellman function
Mutual estimates of Lp-norms and the Bellman function
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Lp 范数和 Bellman 函数的相互估计
DOI：
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发表时间：
2009
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通讯作者：
V. Vasyunin
中科院分区：
文献类型：
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作者：
V. Vasyunin
在本文中，我们描述了一个函数的Lp-范数的范围下固定的Lp-范数与其他两个不同的指数p和下的自然乘法限制的类型的Muckenhoupt条件。这些结果的特殊情况是简单的不等式，如两个Lp-范数之间的插值不等式，以及非平凡的不等式，如Gehring不等式或Mackenhoupt权的逆Hölder不等式。本文的基本方法是寻找相应极值问题的精确Bellman函数。参考书目：5
In this paper, we describe the range of the Lp-norm of a function under fixed Lp-norms with two other different exponents p and under a natural multiplicative restriction of the type of the Muckenhoupt condition. Particular cases of such results are simple inequalities as the interpolation inequality between two Lp-norms as well as such nontrivial inequalities as the Gehring inequality or the reverse Hölder inequality for Mackenhoupt weights. The basic method of our paper is the search for the exact Bellman function of the corresponding extremal problem. Bibliography: 5