Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 841–862

HANKEL BILINEAR FORMS ON GENERALIZED FOCK–SOBOLEV SPACES ON Cⁿ

Carme Cascante, Joan Fàbrega and Daniel Pascuas

Universitat de Barcelona, Departament de Matemàtiques i Informàtica
Gran Via 585, 08071 Barcelona, Spain; cascante 'at' ub.edu

Universitat de Barcelona, Departament de Matemàtiques i Informàtica
Gran Via 585, 08071 Barcelona, Spain; joan_fabrega 'at' ub.edu

Universitat de Barcelona, Departament de Matemàtiques i Informàtica
Gran Via 585, 08071 Barcelona, Spain; daniel_pascuas 'at' ub.edu

Abstract. We characterize the boundedness of Hankel bilinear forms on a product of generalized Fock–Sobolev spaces on Cⁿ with respect to the weight (1 + |z|)sup>ρe^{-α/2|z|^{2l}}, for l ≥ 1, α > 0 and ρ ∈ R. We obtain a weak decomposition of the Bergman kernel with estimates and a Littlewood–Paley formula, which are key ingredients in the proof of our main results. As an application, we characterize the boundedness, compactness and the membership in the Schatten class of small Hankel operators on these spaces.

2010 Mathematics Subject Classification: Primary 47B35, 47B10, 32A37, 30H20, 32A25.

Key words: Bilinear forms, Fock–Sobolev spaces, small Hankel operator, Schatten class operator, Bergman kernel.

Reference to this article: C. Cascante, J. Fàbrega and D. Pascuas: Hankel bilinear forms on generalized Fock–Sobolev spaces on Cⁿ. Ann. Acad. Sci. Fenn. Math. 45 (2020), 841–862.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4546

HANKEL BILINEAR FORMS ON GENERALIZED FOCK–SOBOLEV SPACES ON Cn

Carme Cascante, Joan Fàbrega and Daniel Pascuas

HANKEL BILINEAR FORMS ON GENERALIZED FOCK–SOBOLEV SPACES ON Cⁿ