Coordinatewise multiple summing operators in Banach spaces
Coordinatewise multiple summing operators in Banach spaces
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Banach 空间中的协调多个求和运算符
DOI：
10.1016/j.jfa.2010.01.008
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发表时间：
2010
影响因子：
1.7
通讯作者：
U. Schwarting
中科院分区：
文献类型：
--
作者：
A. Defant;Dumitru Popa;U. Schwarting
我们发明了新的概念coordinatewise多重求和算子在Banach空间中，并使用它来研究各种向量值的扩展著名的Bohnenblust-Hille不等式（原来扩展Littlewood的4/3不等式）。我们的结果对于m-齐次多项式P：∞→ ∞ p的单式系数的可和性以及向量值Dirichlet级数乘积的收敛性理论都有应用.
We invent the new notion of coordinatewise multiple summing operators in Banach spaces, and use it to study various vector valued extensions of the well-know Bohnenblust–Hille inequality (which originally extended Littlewood's 4/3-inequality). Our results have application on the summability of monomial coefficients of m-homogeneous polynomials P:ℓ∞→ℓp, as well as for the convergence theory of products of vector valued Dirichlet series.