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The main aim of this paper is to prove that the maximal operator of MarcinkiewiczFejér means of double Fourier series with respect to the Kaczmarz system is bounded from the dyadic Hardy-Lorentz space Hpq into the Lorentz space Lpq for every p > 2 and 0 < q ∞ 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, σ2n (f , x1, x2) → f (x1, x2) a.e. as n → ∞. Mathematics subject classification (2000): 42C10.

On (H_pq, L_pq)-type inequality of maximal operator of Marcinkiewicz-Fejér means of double Fourier series with respect to the Kaczmarz system