Partial sums of Fourier series
Jean-Pierre Kahane (2005)
Banach Center Publications
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Jean-Pierre Kahane (2005)
Banach Center Publications
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We investigate some convergence and divergence properties of the logarithmic means of quadratic partial sums of double Fourier series of functions, in measure and in the L Lebesgue norm.
George Tephnadze (2015)
Colloquium Mathematicae
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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.
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