On (Hpq, Lpq)-type inequality of maximal operator of Marcinkiewicz-Fejer 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-Fejer 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 < q <= infinity provided that the supremum in the maximal operator is taken over special indices. As a consequence, we obtain the a.e. convergence of Mareinkiewicz-Fejer means of double Fourier series for special indices with respect to the Walsh-Kaczmarz system. That is, sigma(2)n (f, x(1), x(2)) --> f(x(1), x(2)) a.e. as n --> infinity.