On the boundedness of certain operators of convolution type on Fock spaces

Thangavelu, Sundaram

doi:10.1090/proc/17202

On the boundedness of certain operators of convolution type on Fock spaces
HTML articles powered by AMS MathViewer

by Sundaram Thangavelu;

Proc. Amer. Math. Soc.

DOI: https://doi.org/10.1090/proc/17202

Published electronically: April 14, 2025

HTML | PDF | Request permission

Abstract:

We find necessary and sufficient conditions on the convolution kernels $\varphi$ so that certain operators on twisted Fock spaces $\mathcal {F}^\lambda (\mathbb {C}^{2n})$ are bounded.

References

Du-Won Byun, Inversions of Hermite semigroup, Proc. Amer. Math. Soc. 118 (1993), no. 2, 437–445. MR 1145414, DOI 10.1090/S0002-9939-1993-1145414-6
Shubham R. Bais and D. Venku Naidu, $\mathcal {L}$-invariant and radial singular integral operators on the Fock space, J. Pseudo-Differ. Oper. Appl. 14 (2023), no. 1, Paper No. 11, 35. MR 4540871, DOI 10.1007/s11868-023-00506-w
Guangfu Cao, Li He, Ji Li, and Minxing Shen, Boundedness criterion for integral operators on the fractional Fock-Sobolev spaces, Math. Z. 301 (2022), no. 4, 3671–3693. MR 4449725, DOI 10.1007/s00209-022-03050-3
Guangfu Cao, Ji Li, Minxing Shen, Brett D. Wick, and Lixin Yan, A boundedness criterion for singular integral operators of convolution type on the Fock space, Adv. Math. 363 (2020), 107001, 33. MR 4053517, DOI 10.1016/j.aim.2020.107001
Gerald B. Folland, Harmonic analysis in phase space, Annals of Mathematics Studies, vol. 122, Princeton University Press, Princeton, NJ, 1989. MR 983366, DOI 10.1515/9781400882427
Rahul Garg and Sundaram Thangavelu, Boundedness of certain linear operators on twisted Fock spaces, Math. Z. 307 (2024), no. 2, Paper No. 39, 24. MR 4748944, DOI 10.1007/s00209-024-03500-0
Bernhard Krötz, Sundaram Thangavelu, and Yuan Xu, The heat kernel transform for the Heisenberg group, J. Funct. Anal. 225 (2005), no. 2, 301–336. MR 2152501, DOI 10.1016/j.jfa.2005.03.019
Sundaram Thangavelu, Lectures on Hermite and Laguerre expansions, Mathematical Notes, vol. 42, Princeton University Press, Princeton, NJ, 1993. With a preface by Robert S. Strichartz. MR 1215939
Sundaram Thangavelu, An introduction to the uncertainty principle, Progress in Mathematics, vol. 217, Birkhäuser Boston, Inc., Boston, MA, 2004. Hardy’s theorem on Lie groups; With a foreword by Gerald B. Folland. MR 2008480, DOI 10.1007/978-0-8176-8164-7
Sundaram Thangavelu, Gutzmer’s formula and Poisson integrals on the Heisenberg group, Pacific J. Math. 231 (2007), no. 1, 217–237. MR 2304629, DOI 10.2140/pjm.2007.231.217
S. Thangavelu, An analogue of Gutzmer’s formula for Hermite expansions, Studia Math. 185 (2008), no. 3, 279–290. MR 2391022, DOI 10.4064/sm185-3-5
Sundaram Thangavelu, Fourier multipliers and pseudo-differential operators on Fock-Sobolev spaces, Integral Equations Operator Theory 97 (2025), no. 1, Paper No. 2, 21. MR 4842962, DOI 10.1007/s00020-024-02789-0
Sundaram Thangavelu, Algebras of entire functions and representations of the twisted Heisenberg group, Indian J. Pure Appl. Math. 55 (2024), no. 3, 911–921. MR 4798718, DOI 10.1007/s13226-024-00636-x
Brett D. Wick and Shengkun Wu, Integral operators on Fock-Sobolev spaces via multipliers on Gauss-Sobolev spaces, Integral Equations Operator Theory 94 (2022), no. 2, Paper No. 22, 24. MR 4431054, DOI 10.1007/s00020-022-02701-8

AMS Website Down

Proceedings of the American Mathematical Society

On the boundedness of certain operators of convolution type on Fock spaces
HTML articles powered by AMS MathViewer

Abstract: