The below boundedness of matrix operators on the special Lorentz sequence spaces

Let A=(an,k)n,k⩾0 be a non-negative matrix. Denote by Lℓp(w),weakℓq(A) the supremum of those L, satisfying the following inequality:supB{1(#B)1−1q∑n∈B(∑k=0∞an,kxk)}⩾L{∑n=0∞wnxnp}1p, where x={xk}k=0∞∈ℓp(w), x⩾0, w={wn}k=0∞ is a non-negative decreasing sequence and the supremum is taken over all nonempty subset B of non-negative integers with finite cardinal. In this paper we focus on the evaluation of Lℓp(w),weakℓq(At) for a lower triangular matrix A, where 00. A similar result is also established for the case in which (Hμα)t is replaced by Hμα. In particular, we apply our results to summability matrices, weighted mean matrices, Nörlund matrices and some special generalized Hausdorff matrices such as generalized Cesàro, generalized Hölder, generalized Gamma and generalized Euler matrices. Our results provide some analogue to those given by R. Lashkaripour, G. Talebi, Lower bound for matrix operators on the Euler weighted sequence space ew,pθ (0