Fourier-Haar coefficients of function from Marcinkiewicz space

Abstract: 

Let {fn} be an orthogonal, uniformly bounded, normalised system. The classical Mercer theorem states that for every summable function the sequence of its 'Fourier' coefficients with respect to {fn} is converging to zero. The talk addresses the case when {fn} coincides with the classical Haar system, which is not uniformly bounded. The emphasis is made on the analogue of the Mercer theorem for functions from Marcinkiewicz spaces.