Transition from the dyadic to the real nonperiodic Hardy space

Fridli, Sándor (2000) Transition from the dyadic to the real nonperiodic Hardy space. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 16. pp. 1-8. ISSN 0866-0174

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Abstract

The dyadic Hardy space plays a special role in Walsh analysis. Namely, it separates the Lp[0, 1) (1 < p ≤ ∞) and the L1[0, 1) spaces, and in many cases the results received for the (1 < p ≤ ∞) case can be extended for the dyadic Hardy space but not for L1[0, 1). The real nonperiodic Hardy space, which is wider than the dyadic one, is often employed in the trigonometric Fourier analysis. It is natural to ask whether the results proved for the dyadic Hardy space remain true for the real nonperiodic Hardy space. The idea behind this question is to make it possible to compare the corresponding results in the trigonometric and in the Walsh analysis. In this paper we provide a simple method for solving this problem for σ-sublinear functionals. Also, we study two well known sequences of functionals to demonstrate how our method works.

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