Geodesic
On the partial sums of Walsh–Fourier series
George Tephnadze 1
1 Department of Mathematics Faculty of Exact and Natural Sciences Tbilisi State University Chavchavadze St. 1 Tbilisi 0128, Georgia and Department of Engineering Sciences and Mathematics Luleå University of Technology SE-971 87 Luleå, Sweden
Colloquium Mathematicum, Tome 141 (2015) no. 2, pp. 227-242 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We investigate convergence and divergence of specific subsequences of partial sums with respect to the Walsh system on martingale Hardy spaces. By using these results we obtain a relationship of the ratio of convergence of the partial sums of the Walsh series and the modulus of continuity of the martingale. These conditions are in a sense necessary and sufficient.
DOI : 10.4064/cm141-2-7
Keywords: investigate convergence divergence specific subsequences partial sums respect walsh system martingale hardy spaces using these results obtain relationship ratio convergence partial sums walsh series modulus continuity martingale these conditions sense necessary sufficient

George Tephnadze  1

1 Department of Mathematics Faculty of Exact and Natural Sciences Tbilisi State University Chavchavadze St. 1 Tbilisi 0128, Georgia and Department of Engineering Sciences and Mathematics Luleå University of Technology SE-971 87 Luleå, Sweden 
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George Tephnadze. On the partial sums of Walsh–Fourier series. Colloquium Mathematicum, Tome 141 (2015) no. 2, pp. 227-242. doi: 10.4064/cm141-2-7

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