Generalized Hardy spaces on tube domains over cones

Gustavo Garrigos

Colloquium Mathematicae, Tome 89 (2001), p. 213-251 / Harvested from The Polish Digital Mathematics Library

Résumé

We define a class of spaces $H_{μ}^{p}$ , 0 < p < ∞, of holomorphic functions on the tube, with a norm of Hardy type: ${| | F | |}_{H_{μ}^{p}}^{p} = s u p_{y \in Ω} \int_{Ω ̅} \int_{ℝ ⁿ} {| F (x + i (y + t)) |}^{p} d x d μ (t)$ . We allow μ to be any quasi-invariant measure with respect to a group acting simply transitively on the cone. We show the existence of boundary limits for functions in $H_{μ}^{p}$ , and when p ≥ 1, characterize the boundary values as the functions in $L_{μ}^{p}$ satisfying the tangential CR equations. A careful description of the measures μ when their supports lie on the boundary of the cone is also provided.

Publié le : 2001-01-01

Zbl 0999.42014

EUDML-ID : urn:eudml:doc:283814

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     title = {Generalized Hardy spaces on tube domains over cones},
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     volume = {89},
     year = {2001},
     pages = {213-251},
     zbl = {0999.42014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm90-2-4}
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Gustavo Garrigos. Generalized Hardy spaces on tube domains over cones. Colloquium Mathematicae, Tome 89 (2001) pp. 213-251. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm90-2-4/