论文标题
多线性形式的Orlicz不平等
The Orlicz inequality for multilinear forms
论文作者
论文摘要
orlicz $ \ left（\ ell_ {2}，\ ell_ {1} \ right）$不等式指出$$ \ left（\ sum_ {j_ {1} = 1}^1}^{n}^{n} {n} \ left（ }，e_ {j_ {2}}）\ right \ right \ vert \ right） ^{2} \ right） ^{\ frac {\ frac {1} {2}} \ leq leq \ sqrt {2} \ left pert \ vert a \ pert a \ right \ vert $$ $ a：\ mathbb {k}^{n} \ times \ times \ mathbb {k}^{n} \ rightarrow \ rightarrow \ mathbb {k} $和所有积极的integers $ n $，其中$ \ mathbb {k} $ \ mathbb {c}^{n} $具有至上的标准。在本文中，我们将这种不等式扩展到多线性表单，并使用$ \ mathbb {k}^{n} $赋予所有$ p \ in \ lbrack1，\ infty]的$ \ ell_ {p} $ norms。
The Orlicz $\left( \ell_{2},\ell_{1}\right) $-mixed inequality states that $$ \left( \sum_{j_{1}=1}^{n}\left( \sum_{j_{2}=1}^{n}\left\vert A(e_{j_{1} },e_{j_{2}})\right\vert \right) ^{2}\right) ^{\frac{1}{2}}\leq\sqrt {2}\left\Vert A\right\Vert $$ for all bilinear forms $A:\mathbb{K}^{n}\times\mathbb{K}^{n}\rightarrow \mathbb{K}$ and all positive integers $n$, where $\mathbb{K}^{n}$ denotes $\mathbb{R}^{n}$ or $\mathbb{C}^{n}$ endowed with the supremum norm. In this paper we extend this inequality to multilinear forms, with $\mathbb{K}^{n}$ endowed with $\ell_{p}$ norms for all $p\in\lbrack1,\infty].$
