Abstract
In this paper we consider the martingale Hardy spaces defined with the help of the mixed Lp→-norm. Using atomic decomposition and Doob's inequality, some applications will be shown in Fourier-analysis, such as the uniform boundedness of the partial sums of the Walsh-Fourier series on Lp→(1<p→<∞) and the boundedness of the Fejér maximal operator from Hp→ to Lp→(1/2<p→<∞). As a consequence of the boundedness, we get some almost everywhere and norm convergence results.
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