A Hardy space related to the square root of the Poisson kernel

Jonatan Vasilis

Jonatan Vasilis

Studia Mathematica, Tome 196 (2010), p. 207-225 / Harvested from The Polish Digital Mathematics Library

Résumé

A real-valued Hardy space $H ¹_{\sqrt} () \subseteq L ¹ ()$ related to the square root of the Poisson kernel in the unit disc is defined. The space is shown to be strictly larger than its classical counterpart H¹(). A decreasing function is in $H ¹_{\sqrt} ()$ if and only if the function is in the Orlicz space LloglogL(). In contrast to the case of H¹(), there is no such characterization for general positive functions: every Orlicz space strictly larger than L log L() contains positive functions which do not belong to $H ¹_{\sqrt} ()$ , and no Orlicz space of type Δ₂ which is strictly smaller than L¹() contains every positive function in $H ¹_{\sqrt} ()$ . Finally, we have a characterization of certain eigenfunctions of the hyperbolic Laplace operator in terms of $H ¹_{\sqrt} ()$ .

Publié le : 2010-01-01

Zbl 1221.42041

EUDML-ID : urn:eudml:doc:285512

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     year = {2010},
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Jonatan Vasilis. A Hardy space related to the square root of the Poisson kernel. Studia Mathematica, Tome 196 (2010) pp. 207-225. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-3-1/