A Hankel matrix acting on Hardy and Bergman spaces

• Autorzy: Petros Galanopoulos , José Ángel Peláez
• Języki publikacji: EN

Abstrakty

EN

Let μ be a finite positive Borel measure on [0,1). Let $ℋ_{μ} = (μ_{n,k})_{n,k≥0}$ be the Hankel matrix with entries $μ_{n,k} = ∫_{[0,1)} t^{n+k} dμ(t)$. The matrix $𝓗_{μ}$ induces formally an operator on the space of all analytic functions in the unit disc by the fomula
$ℋ_{μ}(f)(z) = ∑_{n=0}^{∞}i (∑_{k=0}^{∞} μ_{n,k}a_{k})zⁿ$, z ∈ 𝔻,
where $f(z) = ∑_{n=0}^{∞} aₙzⁿ$ is an analytic function in 𝔻.
We characterize those positive Borel measures on [0,1) such that $ℋ_{μ}(f)(z) = ∫_{[0,1)} f(t)/(1-tz) dμ(t)$ for all f in the Hardy space H¹, and among them we describe those for which $ℋ_{μ}$ is bounded and compact on H¹. We also study the analogous problem for the Bergman space A².

Kategorie tematyczne

• 30H10: Hardy spaces
• 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 200
• Numer: 3
• Strony: 201-220

Daty

wydano

2010

Twórcy

autor

Petros Galanopoulos

• Departamento de Análisis Matemático, Universidad de Málaga, Campus de Teatinos, 29071 Málaga, Spain

autor

José Ángel Peláez

• Departamento de Análisis Matemático, Universidad de Málaga, Campus de Teatinos, 29071 Málaga, Spain

Identyfikatory

DOI

10.4064/sm200-3-1