The main aim of this paper is to prove that the maximal operator σ0k*:= supn ∣σn,nk∣ of the Fej�r means of double Fourier series with respect to the Kaczmarz system is not bounded from the Hardy space H1/2 to the space weak-L1/2.
The aim of this paper is to prove the a.e. convergence of sequences of the Fejér means of the Walsh–Fourier series of bivariate integrable functions. That is, let such that aj(n+1)≧δsupk≦naj(n) (j=1,2, n∊ℕ) for some δ>0 and a1(+∞)=a2(+∞)=+∞. Then for each integrable function f∊L1(I2) we have the a.e. relation . It will be a straightforward and easy consequence of this result the cone restricted a.e. convergence of the two-dimensional Walsh–Fejér means of integrable functions which was proved earlier by the author and Weisz [3,8].
The main aim of this paper is to prove that there exists a martingale f ∈ H12/▭ such that the restricted maximal operators of Fejér means of twodimensional Walsh-Fourier series and conjugate Walsh-Fourier
series does not belong to the space weak-L1/2.