Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl

PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
• # Artykuł - szczegóły

## Studia Mathematica

2010 | 199 | 3 | 207-225

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

EN

### Abstrakty

EN
A real-valued Hardy space $H¹_{√}(𝕋) ⊆ L¹(𝕋)$ 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(𝕋). A decreasing function is in $H¹_{√}(𝕋)$ if and only if the function is in the Orlicz space LloglogL(𝕋). In contrast to the case of H¹(𝕋), there is no such characterization for general positive functions: every Orlicz space strictly larger than L log L(𝕋) contains positive functions which do not belong to $H¹_{√}(𝕋)$, and no Orlicz space of type Δ₂ which is strictly smaller than L¹(𝕋) contains every positive function in $H¹_{√}(𝕋)$. Finally, we have a characterization of certain eigenfunctions of the hyperbolic Laplace operator in terms of $H¹_{√}(𝕋)$.

207-225

wydano
2010

### Twórcy

autor
• Department of Mathematical Sciences, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
• Department of Mathematical Sciences, University of Gothenburg, SE-412 96 Göteborg, Sweden