We study some new summability properties of multilinear operators. We introduce the concepts of φ‐summing, φ semi‐integral and φ‐dominated multilinear maps generated by Orlicz functions. We prove a variant of Pietsch's domination theorem for φ‐summing operators, providing also a characterization of φ‐dominated operators in terms of factorizations. We analyze vector‐valued inequalities associated to these maps, which are applied to obtain general variants of multiple summing operators. We also study translation invariant multilinear operators acting in products of spaces of continuous functions, proving that a factorization theorem can be obtained for them as a consequence of a suitable representation of the corresponding normalized Haar measure.

中文翻译：

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通过Orlicz空间和平移不变算子进行多线性映射的理想选择

我们研究了多线性算子的一些新的可加性。我们介绍了由Orlicz函数生成的φ求和，φ半积分和φ为主的多线性映射的概念。我们证明了φ求和算子的Pietsch支配定理的一个变体，并提供了分解为因数的φ算子的特征。我们分析了与这些映射关联的向量值不等式，这些不等式用于获取多个求和运算符的一般变体。我们还研究了在连续函数空间的乘积中作用的平移不变多线性算子，证明了由于相应归一化Haar测度的适当表示，可以为它们获得因式分解定理。