Let E=(E_{n,k})_{n,kgeq 0} be an invertible summability matrix with bounded absolute row sums and column sums, and let E_{p} denote the domain of E in the sequence space ell _{p}(1le p<infty ). In this paper, we consider the transpose of Nörlund matrix associated with a nonnegative and nonincreasing sequence as an operator mapping ell _{p} into the sequence space E_{p} and establish a general upper estimate for its operator norm, which depends on the ell _{1}-norm of the rows and columns of the matrix E. In particular, we apply our result to domains of some summability matrices such as Fibonacci, Karamata, Euler, and Taylor matrices. Our result is an extension of those given by G. Talebi and M.A. Dehghan (Linear Multilinear Algebra 64(2):196–207, 2016). It also provides some analogues of the results by G. Talebi (Indag. Math. 28(3):629–636, 2017).