We prove that certain means of quadratic partial sums of the two-dimensional Walsh–Fourier series are uniformly bounded operators acting from the Hardy space H p to the space L p for 0 < p < 1.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 6, pp. 822–834, June, 2013.
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Tephnadze, G. Strong Convergence of Two-Dimensional Walsh–Fourier Series. Ukr Math J 65, 914–927 (2013). https://doi.org/10.1007/s11253-013-0828-0
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DOI: https://doi.org/10.1007/s11253-013-0828-0