It is well known that not every summability property for multilinear operators leads to a
factorization theorem. In this paper we undertake a detailed study of factorization schemes
for summing linear and nonlinear operators. Our aim is to integrate under the same theory a
wide family of classes of mappings for which a Pietsch type factorization theorem holds. Our
construction includes the cases of absolutely p-summing linear operators,(p, σ)-absolutely
continuous linear operators, factorable strongly p-summing multilinear operators,(p 1,..., pn) …

It is well known that not every summability property for non linear operators leads to a
factorization theorem. In this paper we undertake a detailed study of factorization schemes
for summing linear and nonlinear operators. Our aim is to integrate under the same theory a
wide family of classes of mappings for which a Pietsch type factorization theorem holds. We
analyze the class of linear operators that are defined by a summability inequality involving a
homogeneous map. Our construction includes the cases of absolutely $ p $-summing linear …