Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 89-107

BOUNDEDNESS OF VOLTERRA OPERATORS ON SPACES OF ENTIRE FUNCTIONS

Oscar Blasco

Universidad de Valencia, Departamento de Análisis Matemático
46100 Burjassot, Valencia, Spain; oblasco 'at' uv.es

Abstract. In this paper we find some necessary and sufficient conditions on an entire function g for the Volterra operator V_g(f)(z) = ∫₀^zf(ξ)g'(ξ)dξ to be bounded between different weighted spaces of entire functions H_v^∞(C) or Fock-type spaces F_p^φ(C).

2010 Mathematics Subject Classification: Primary 47G10; Secondary 30H20, 47B07, 47B37, 47B38, 30D15, 30D20, 46E15.

Key words: Volterra operator, weighted spaces, entire function, Fock-type spaces.

Reference to this article: O. Blasco: Boundedness of Volterra operators on spaces of entire functions. Ann. Acad. Sci. Fenn. Math. 43 (2018), 89-107.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4303