2-Lipschitz Pietsch-q-integral and 2-Lipschitz q-nuclear operators

In this paper, we extend the concept of q-nuclear to $2$-Lipschitz mappings. We provide a factorization theorem and establish that a $2$-Lipschitz operator is q-nuclear if and only if its transpose is well-defined and q-nuclear. Additionally, we introduce the concept of $2$-Lipschitz Pietsch-q-integral operators, present a factorization theorem, and demonstrate that this class of operators is generated by the composition method. Conclusively, we demonstrate that every $2$-Lipschitz q-nuclear operator is a $2$-Lipschitz Pietsch-q-integral operator.