On Fourier-Haar coefficients of the function from the Marcinkiewicz space

The main objective of the paper is to describe asymptotic behaviour of Fourier-Haar coefficients of functions from Marcinkiewicz spaces. We also discuss the Cesàro summability and the almost convergence of sequences related to Fourier-Haar coefficients and generalise a result from [17]. Some analogues of Mercer's theorem for Fourier coefficients are proved.