Two new classes of summing multilinear operators, factorable $(q, p)$-summing operators and $(r; p, q)$-summing operators are studied. These classes are described in terms of factorization. It is shown that operators in the first (resp., the second) class admit the factorization through the injective tensor product of Banach spaces (resp., through some Banach lattices). Applications in different contexts related to Grothendieck Theorem and Fourier integral bilinear operators are shown. Motivated by Pisier’s Theorem on factorization of $(q, 1)$-summing operators from $C(K)$-spaces through Lorentz spaces $L_{q,1}$ on some probability Borel measure spaces, we prove two variants of Pisier’s Theorem for bilinear operators on the product of $C(K)$-spaces. We also prove bilinear versions of Mityagin–Pełczyński and Kislyakov Theorems.

中文翻译：

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一些新型多线性算子的因式分解定理

研究了两类新的求和多线性算子，可分解的$（q，p）$-求和算子和$（r; p，q）$-求和算子。这些类是根据分解进行描述的。结果表明，第一类（分别是第二类）中的算子通过Banach空间的内射张量积（分别通过某些Banach格）接受因式分解。显示了在与Grothendieck定理和Fourier积分双线性算子相关的不同上下文中的应用。根据Pisier定理，在一定概率的Borel度量空间上从$ C（K）$空间到Lorentz空间$ L_ {q，1} $的$（q，1）$加和运算符的因式分解，我们证明了Pisier's的两个变体$ C（K）$-空间积的双线性算子定理。我们还证明了Mityagin–Pełczyński和Kislyakov定理的双线性形式。