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

• Autorzy: Jonatan Vasilis
• Języki publikacji: 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 $H¹_{√}(𝕋)$.

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory
• 31A10: Integral representations, integral operators, integral equations methods
• 42B30: H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 199
• Numer: 3
• Strony: 207-225

Daty

wydano

2010

Twórcy

autor

Jonatan Vasilis

• 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

Identyfikatory

DOI

10.4064/sm199-3-1