Nonlinear variants of a theorem of Kwapień

A famous result of S. Kwapień asserts that a linear operator from Banach space to Hilbert is absolutely 1-summing whenever its adjoint q-summing for some 1 ≤ q < ∞; this was recently extended Lipschitz operators by Chen and Zheng. In the present paper we show Kwapień’s Chen-Zheng’s theorems hold in very relaxed nonlinear environment, under weaker hypotheses. Even when restricted original case, our generalizes theorem because it holds just almost summing. addition, variant \({{\cal L}_p}\)-spaces, with p ≥ 2, instead spaces, provided.