Displaying similar documents to “Walsh-Marcinkiewicz means and Hardy spaces”

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 ) .

Thickness conditions and Littlewood-Paley sets

Vladimir Lebedev (2014)

Studia Mathematica

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We consider sets in the real line that have Littlewood-Paley properties LP(p) or LP and study the following question: How thick can these sets be?

Cesàro summability of one- and two-dimensional trigonometric-Fourier series

Ferenc Weisz (1997)

Colloquium Mathematicae

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We introduce p-quasilocal operators and prove that if a sublinear operator T is p-quasilocal and bounded from L ∞ to L ∞ then it is also bounded from the classical Hardy space H p ( T ) to L p (0 < p ≤ 1). As an application it is shown that the maximal operator of the one-parameter Cesàro means of a distribution is bounded from H p ( T ) to L p (3/4 < p ≤ ∞) and is of weak type ( L 1 , L 1 ) . We define the two-dimensional dyadic hybrid Hardy space H 1 ♯ ( T 2 ) and verify that the maximal operator of the Cesàro means of a two-dimensional...