On Approximation of Tensor Products Operators Sequences Associated with Walsh-Paley System

This paper deals with the investigation of the approximation of the weighted Walsh-Fourier series associated with tensor products. In the current work, we investigate the rate of convergence of a sequence of operators in terms of the moduli of partial and mixed continuity. The obtained result allows to find necessary three conditions for the sequence of operators to converge in the $$L_{1}$$ -norm. As a particular application, we resolve M ricz’s problem for rectangular partial sums. Furthermore, we derive a necessary and sufficient condition that ensures the $$L_{1}$$ -norm convergence of a sequence of operators, given in terms of the total modulus of continuity.