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

Jonatan Vasilis. "A Hardy space related to the square root of the Poisson kernel." Studia Mathematica 199.3 (2010): 207-225. <http://eudml.org/doc/285512>.

@article{JonatanVasilis2010,
abstract = {A real-valued Hardy space $H¹_\{√\}() ⊆ L¹()$ 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 $H¹_\{√\}()$ 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 $H¹_\{√\}()$, and no Orlicz space of type Δ₂ which is strictly smaller than L¹() contains every positive function in $H¹_\{√\}()$. Finally, we have a characterization of certain eigenfunctions of the hyperbolic Laplace operator in terms of $H¹_\{√\}()$.},
author = {Jonatan Vasilis},
journal = {Studia Mathematica},
keywords = {Hardy space; Poisson kernel; },
language = {eng},
number = {3},
pages = {207-225},
title = {A Hardy space related to the square root of the Poisson kernel},
url = {http://eudml.org/doc/285512},
volume = {199},
year = {2010},
}

TY - JOUR
AU - Jonatan Vasilis
TI - A Hardy space related to the square root of the Poisson kernel
JO - Studia Mathematica
PY - 2010
VL - 199
IS - 3
SP - 207
EP - 225
AB - A real-valued Hardy space $H¹_{√}() ⊆ L¹()$ 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 $H¹_{√}()$ 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 $H¹_{√}()$, and no Orlicz space of type Δ₂ which is strictly smaller than L¹() contains every positive function in $H¹_{√}()$. Finally, we have a characterization of certain eigenfunctions of the hyperbolic Laplace operator in terms of $H¹_{√}()$.
LA - eng
KW - Hardy space; Poisson kernel;
UR - http://eudml.org/doc/285512
ER -