Hankel operators and weak factorization for Hardy-Orlicz spaces

• Autorzy: Aline Bonami , Sandrine Grellier
• Języki publikacji: EN

Abstrakty

EN

We study the holomorphic Hardy-Orlicz spaces $𝓗 ^{Φ}(Ω)$, where Ω is the unit ball or, more generally, a convex domain of finite type or a strictly pseudoconvex domain in ℂⁿ. The function Φ is in particular such that $𝓗 ¹(Ω)⊂ 𝓗 ^{Φ}(Ω)⊂ 𝓗 ^{p}(Ω)$ for some p > 0. We develop maximal characterizations, atomic and molecular decompositions. We then prove weak factorization theorems involving the space BMOA(Ω). As a consequence, we characterize those Hankel operators which are bounded from $𝓗 ^Φ(Ω)$ into 𝓗 ¹(Ω).

Kategorie tematyczne

• 32A37: Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
• 32A35: H p -spaces, Nevanlinna spaces
• 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 118
• Numer: 1
• Strony: 107-132

Daty

wydano

2010

Twórcy

autor

Aline Bonami

• Fédération Denis Poisson (MAPMO-UMR 6628), Département de Mathématiques, Université d'Orléans, 45067 Orléans Cedex 2, France

autor

Sandrine Grellier

• Fédération Denis Poisson (MAPMO-UMR 6628), Département de Mathématiques, Université d'Orléans, 45067 Orléans Cedex 2, France

Identyfikatory

DOI

10.4064/cm118-1-5