Abstract. In this paper we prove that there exists a continuous function on $[0,1)^2$, with a certain smoothness, whose double Fourier--Walsh--Paley series diverges by rectangles on a set of positive measure.

DOI: 10.14232/actasm-019-319-0

AMS Subject Classification (1991): 42C10

Keyword(s): Walsh--Paley, double Fourier series, divergence a.e

received 9.6.2019, revised 8.1.2020, accepted 14.1.2020. (Registered under 69/2019.)