On Almost Everywhere Covergence of Dyadic Fourier Series in L2

The almost everywhere convergence of the dyadic Fourier series in L2 is studied. The logarithmic behaviour of the partial sums of Dyadic Fourier series in L2 is established. In order to obtain the estimation for the maximal operator corresponding to the dyadic Fourier series, the properties and asymptotical behaviour of the Dirichlet kernel are investigated. The general representation in the dyadic group and the properties of the characteristic set are used