Generalized Hardy spaces on tube domains over cones

• Autorzy: Gustavo Garrigos
• Języki publikacji: EN

Abstrakty

EN

We define a class of spaces $H^{p}_{μ}$, 0 < p < ∞, of holomorphic functions on the tube, with a norm of Hardy type:
$||F||^{p}_{H^{p}_{μ}} = sup_{y∈Ω} ∫_{Ω̅} ∫_{ℝⁿ} |F(x+i(y+t))|^{p} dxdμ(t)$.
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 $H^{p}_{μ}$, and when p ≥ 1, characterize the boundary values as the functions in $L^{p}_{μ}$ 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.

Kategorie tematyczne

• 32M15: Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras
• 42B30: H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2001
• Tom: 90
• Numer: 2
• Strony: 213-251

Daty

wydano

2001

Twórcy

autor

Gustavo Garrigos

• Université d'Orléans, MAPMO-BP 6759, 45067 Orléans Cedex 2, France
• Facultad de Ciencias C-XV, Universidad Autónoma de Madrid, 28049 Madrid, Spain

Identyfikatory

DOI

10.4064/cm90-2-4