Generalized Hardy spaces on tube domains over cones

Gustavo Garrigos. "Generalized Hardy spaces on tube domains over cones." Colloquium Mathematicae 90.2 (2001): 213-251. <http://eudml.org/doc/283814>.

@article{GustavoGarrigos2001,
abstract = {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.},
author = {Gustavo Garrigos},
journal = {Colloquium Mathematicae},
keywords = {Hardy space; symmetric cone; Riesz distributions; tangential CR equations},
language = {eng},
number = {2},
pages = {213-251},
title = {Generalized Hardy spaces on tube domains over cones},
url = {http://eudml.org/doc/283814},
volume = {90},
year = {2001},
}

TY - JOUR
AU - Gustavo Garrigos
TI - Generalized Hardy spaces on tube domains over cones
JO - Colloquium Mathematicae
PY - 2001
VL - 90
IS - 2
SP - 213
EP - 251
AB - 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.
LA - eng
KW - Hardy space; symmetric cone; Riesz distributions; tangential CR equations
UR - http://eudml.org/doc/283814
ER -