Coordinatewise multiple summing operators in Banach spaces

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• 作者：Andreas Defant ; Dumitru Popa ; Ursula Schwarting
• 关键词：Bohnenblust– ; Hille inequality ; Multiple summing operators ; Polynomials ; Dirichlet series
• 刊名：Journal of Functional Analysis
• 出版年：2010
• 出版时间：1 July 2010
• 年：2010
• 卷：259
• 期：1
• 页码：220-242
• 全文大小：242 K

文摘

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_∞→ℓ_p, as well as for the convergence theory of products of vector valued Dirichlet series.