Bounded operators on weighted spaces of holomorphic functions on the upper half-plane

• Autorzy: Mohammad Ali Ardalani , Wolfgang Lusky
• Języki publikacji: EN

Abstrakty

EN

Let v be a standard weight on the upper half-plane 𝔾, i.e. v: 𝔾 → ]0,∞[ is continuous and satisfies v(w) = v(i Im w), w ∈ 𝔾, v(it) ≥ v(is) if t ≥ s > 0 and $lim_{t→ 0} v(it) = 0$. Put v₁(w) = Im wv(w), w ∈ 𝔾. We characterize boundedness and surjectivity of the differentiation operator D: Hv(𝔾) → Hv₁(𝔾). For example we show that D is bounded if and only if v is at most of moderate growth. We also study composition operators on Hv(𝔾).

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 47B38: Operators on function spaces (general)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 209
• Numer: 3
• Strony: 225-234

Daty

wydano

2012

Twórcy

autor

Mohammad Ali Ardalani

• Department of Mathematics, Faculty of Science, University of Kurdistan, Pasdaran Ave., Postal code: 66177-15175, Sanandaj, Iran

autor

Wolfgang Lusky

• Institute for Mathematics, University of Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany

Identyfikatory

DOI

10.4064/sm209-3-2