The Hausdorff operators on the real Hardy spaces Hp(ℝ)
Yuichi Kanjin
Studia Mathematica, Tome 147 (2001), p. 37-45 / Harvested from The Polish Digital Mathematics Library
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We prove that the Hausdorff operator generated by a function ϕ is bounded on the real Hardy space Hp(ℝ), 0 < p ≤ 1, if the Fourier transform ϕ̂ of ϕ satisfies certain smoothness conditions. As a special case, we obtain the boundedness of the Cesàro operator of order α on Hp(ℝ), 2/(2α+1) < p ≤ 1. Our proof is based on the atomic decomposition and molecular characterization of Hp(ℝ).

Publié le : 2001-01-01
EUDML-ID : urn:eudml:doc:285356 
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Yuichi Kanjin. The Hausdorff operators on the real Hardy spaces $H^{p}(ℝ)$
            . Studia Mathematica, Tome 147 (2001) pp. 37-45. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm148-1-4/