As main result we prove that certain means of the partial sums of two-parameter Vilenkin-Fourier series are uniformly bounded operators from Hp to Lp (0 < p ≦ 1). The Hardy space Hp (0 < p ≦ 1) will be defined by means of a diagonal maximal function. As a consequence we obtain a so-called strong convergence theorem for the Vilenkin-Fourier partial sums. Some dual inequalities are also verified for BMO spaces.
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