On (H_pq, L_pq)-type inequality of maximal operator of marcinkiewicz-fejér means of double fourier series with respect to the Kaczmarz system

The main aim of this paper is to prove that the maximal operator of Marcinkiewicz-Fejér means of double Fourier series with respect to the Kaczmarz system is bounded from the dyadic Hardy-Lorentz space H_pq into the Lorentz space L_pq for every p > 1/2 and 0 < g ≤ ∞ provided that the supremum in the maximal operator is taken over special indices. As a consequence, we obtain the a.e. convergence of Marcinkiewicz-Fejér means of double Fourier series for special indices with respect to the Walsh-Kaczmarz system. That is, σ_2n (f, x¹, x²) → f(x¹, x²) a.e. as n → ∞.