Unified Grothendieck's and Kwapień's theorems for multilinear operators (Q6145794)

If \(m\), \(n\) are natural numbers, \(T:l_{1}\times \cdots \times l_{1}\rightarrow l_{p}\) (\(l_{1}\) appear \(m\)-times) and \(A_{1},\dots,A_{m}:l_{ \infty }\times \cdots \times l_{\infty }\rightarrow l_{1}\) (\( l_{\infty }\) appear \(n\)-times) are bounded multilinear operators, in [\textit{A. Defant} et al., J. Funct. Anal. 259, No. 1, 220--242 (2010; Zbl 1205.46026)] and [\textit{F. Bayart} et al., Collect. Math. 71, No. 2, 301--318 (2020; Zbl 1446.46029)], was studied the problem to find what kind of summability properties have the composition \(T\circ \left( A_{1},\dots,A_{m}\right) \). In the present paper the authors proves some new results in this direction. Their proofs use mainly the technique from the paper of F. Bayart, D. Pellegrino, P. Rueda.