Almost everywhere convergence and divergence of Cesàro means with varying parameters of Walsh–Fourier series

In the present paper, we prove the almost everywhere convergence and divergence of subsequences of Cesàro means with zero tending parameters of Walsh–Fourier series.

Pointwise convergence of certain continuous-time double ergodic averages

We prove almost everywhere convergence of continuous-time quadratic averages with respect to two commuting $\mathbb {R}$ -actions, coming from a single jointly measurable measure-preserving $\mathbb {R}^2$ -action on a probability space. The key ingredient of the proof comes from recent work on multilinear singular integrals; more specifically, from the study of a curved model for the triangular Hilbert transform.

Almost everywhere convergence of Cesàro means of two variable Walsh – Fourier series with varying parameteres

UDC 517.5 We prove that the maximal operator of some means of cubical partial sums of two variable Walsh – Fourier series of integrable functions is of weak type . Moreover, the -means of the function converge a.e. to for , where is the Walsh group for some sequences .

Maximal summability operators on the dyadic hardy spaces

It is proved that the maximal operators of subsequences of N?rlund logarithmic means and Ces?ro means with varying parameters of Walsh-Fourier series is bounded from the dyadic Hardy spaces Hp to Lp. This implies an almost everywhere convergence for the subsequences of the summability means.