Inequalities for $$L^p$$-Norms that Sharpen the Triangle Inequality and Complement Hanner’s Inequality
Inequalities for $$L^p$$-Norms that Sharpen the Triangle Inequality and Complement Hanner’s Inequality
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$$L^p$$ 的不等式 - 锐化三角不等式并补充汉纳不等式的规范
DOI：
10.1007/s12220-020-00425-y
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Lieb, Elliott H.
中科院分区：
文献类型：
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作者：
Carlen, Eric A.;Frank, Rupert L.;Ivanisvili, Paata;Lieb, Elliott H.
在2006年Carbery提出了一个问题，改进了任何测度空间的两个函数fandgin的朴素范数不等式。当这是一个等式，但是当两个边的支撑不相交时，就不需要这个因子了。Carbery的问题涉及两种情况之间的插值，插值参数测量重叠。Carbery证明了他提出的不等式在特殊情况下成立。在这里，我们证明了不等式的所有功能，事实上，我们证明了不等式的这种类型是强于一个Carbery提出。此外，我们的强不等式对所有实数都有效。
In 2006 Carbery raised a question about an improvement on the naïve norm inequalityfor two functionsfandginof any measure space. Whenthis is an equality, but when the supports offandgare disjoint the factoris not needed. Carbery’s question concerns a proposed interpolation between the two situations forwith the interpolation parameter measuring the overlap being. Carbery proved that his proposed inequality holds in a special case. Here, we prove the inequality for all functions and, in fact, we prove an inequality of this type that is stronger than the one Carbery proposed. Moreover, our stronger inequalities are valid forallreal.