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Maximal operators of Fejér-Walsh means. (English) Zbl 1199.42127

Summary: The main aim of this paper is to prove that the maximal operator \(\tilde \sigma{}^* f:=\sup_{n\in P}\frac{| \sigma_n f| }{\log^2(n+1)}\) is bounded from the Hardy space \(H_{1/2}\) to the space \(L_{1/2}\).

MSC:

42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
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