Complex Analysis and Operator Theory

, Volume 13, Issue 3, pp 935–958 | Cite as

Integral, Differential and Multiplication Operators on Generalized Fock Spaces

  • Tesfa MengestieEmail author
  • Sei-Ichiro Ueki


Volterra companion integral and multiplication operators with holomorphic symbols are studied for a large class of generalized Fock spaces on the complex plane \(\mathbb {C}\). The weights defining these spaces are radial and subject to a mild smoothness condition. In addition, we assumed that the weights decay faster than the classical Gaussian weight. One of our main results show that there exists no nontrivial holomorphic symbols g which induce bounded Volterra companion integral \(I_g\) and multiplication operators \(M_g\) acting between the weighted spaces. We also describe the bounded and compact Volterra-type integral operators \(V_g\) acting between \({\mathcal {F}}_q^\psi \) and \({\mathcal {F}}_p^\psi \) when at least one of the exponents p or q is infinite, and extend results of Constantin and Peláez for finite exponent cases. Furthermore, we showed that the differential operator D acts in unbounded fashion on these and the classical Fock spaces.


Weighted Fock space Generalized Fock spaces Volterra operator Multiplication operator Differential operator Bounded Compact 

Mathematics Subject Classification

Primary 47B32 30H20 Secondary 46E22 46E20 47B33 



We would like to thank the referee for careful review of our paper and pointing us relevant literatures, which eventually helped us put our work in context to already known results.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesWestern Norway University of Applied SciencesStordNorway
  2. 2.Toki UniversityHitachiJapan

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