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Displaying similar documents to “On the direct kernels with respect to the Walsh-Kaczmarz system.”

Walsh-Marcinkiewicz means and Hardy spaces

Károly Nagy, George Tephnadze (2014)

Open Mathematics

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The main aim of this paper is to investigate the Walsh-Marcinkiewicz means on the Hardy space H p, when 0 < p < 2/3. We define a weighted maximal operator of Walsh-Marcinkiewicz means and establish some of its properties. With its aid we provide a necessary and sufficient condition for convergence of the Walsh-Marcinkiewicz means in terms of modulus of continuity on the Hardy space H p, and prove a strong convergence theorem for the Walsh-Marcinkiewicz means.

On the maximal operator of Walsh-Kaczmarz-Fejér means

Ushangi Goginava, Károly Nagy (2011)

Czechoslovak Mathematical Journal

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In this paper we prove that the maximal operator σ ˜ κ , * f : = sup n ∈ ℙ | σ n κ f | log 2 ( n + 1 ) , where σ n κ f is the n -th Fejér mean of the Walsh-Kaczmarz-Fourier series, is bounded from the Hardy space H 1 / 2 ( G ) to the space L 1 / 2 ( G ) .