Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 227-257

PSEUDO-DIFFERENTIAL CALCULUS IN A BARGMANN SETTING

Nenad Teofanov and Joachim Toft

University of Novi Sad, Department of Mathematics and Informatics
Novi Sad, Serbia; nenad.teofanov 'at' dmi.uns.ac.rs

Linnæus University, Department of Mathematics
Växjö, Sweden; joachim.toft 'at' lnu.se

Abstract. We give a fundament for Berezin's analytic Ψdo considered in [4] in terms of Bargmann images of Pilipović spaces. We deduce basic continuity results for such Ψdo, especially when the operator kernels are in suitable mixed weighted Lebesgue spaces and act on certain weighted Lebesgue spaces of entire functions. In particular, we show how these results imply well-known continuity results for real Ψdo with symbols in modulation spaces, when acting on other modulation spaces.

2010 Mathematics Subject Classification: Primary 32W25, 35S05, 32A17, 46F05, 42B35; Secondary 32A25, 32A05.

Key words: Analytic kernels, Berezin operators, Pilipović spaces, modulation spaces, Gelfand–Shilov spaces.

Reference to this article: N. Teofanov and J. Toft: Pseudo-differential calculus in a Bargmann setting. Ann. Acad. Sci. Fenn. Math. 45 (2020), 227-257.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4512