Strong convergence theorems for \(H_p(\mathbb T \times \dots \times \mathbb T)\) (Q2754960)

The author investigates multiplier operators on the Hardy space \(H_p(\mathbb T\times\dots\times \mathbb T)\), proves Bernstein's inequality for multi-parameter trigonometric polynomials. The author also proves that some means of the partial sums of the multi-parameter trigonometric Fourier series are uniformly bounded operators from the Hardy space \(H_p(\mathbb T\times\dots\times \mathbb T)\) to the Lebesgue space \(L_p\) for \(1/2<p\leq 1\). As a consequence he obtaines some strong convergence theorems concerning the partial sums. The dual inequalities are also verified, and a Marcinkiewicz-Zygmund-type inequality is obtained for \(BMO\) spaces.