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

Studia Mathematica (2010)

- Volume: 199, Issue: 3, page 207-225
- ISSN: 0039-3223

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topJonatan 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 -

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