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arxiv: 1504.05975 · v1 · pith:32RDZ2P7new · submitted 2015-04-21 · 🧮 math.CA

Strong convergence theorem of Ces\`aro means with respect to the Walsh system

classification 🧮 math.CA
keywords meansalphaboundedconvergencehardyleftmartingaleone-dimensional
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We prove that Ces\`{a}ro means of one-dimensional Walsh-Fourier series are uniformly bounded operators in the martingale Hardy space $H_{p}$ for $% 0<p<1/\left( 1+\alpha \right).$

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