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@article{2262457,
author = {Ding, Chao and Nguyen, Phuoc Tai and John, Ryan},
article_number = {4},
doi = {http://dx.doi.org/10.1017/S0013091522000426},
keywords = {Bosonic Laplacians; real analyticity; L-2 decomposition; bosonic Hardy spaces; bosonic Bergman spaces},
language = {eng},
issn = {0013-0915},
journal = {Proceedings of the Edinburgh Mathematical Society},
title = {Polynomial null solutions to bosonic Laplacians, bosonic bergman and hardy spaces},
url = {https://doi.org/10.1017/S0013091522000426},
volume = {65},
year = {2022}
}
TY - JOUR
ID - 2262457
AU - Ding, Chao - Nguyen, Phuoc Tai - John, Ryan
PY - 2022
TI - Polynomial null solutions to bosonic Laplacians, bosonic bergman and hardy spaces
JF - Proceedings of the Edinburgh Mathematical Society
VL - 65
IS - 4
SP - 958-989
EP - 958-989
PB - Cambridge University Press
SN - 00130915
KW - Bosonic Laplacians
KW - real analyticity
KW - L-2 decomposition
KW - bosonic Hardy spaces
KW - bosonic Bergman spaces
UR - https://doi.org/10.1017/S0013091522000426
N2 - A bosonic Laplacian, which is a generalization of Laplacian, is constructed as a second-order conformally invariant differential operator acting on functions taking values in irreducible representations of the special orthogonal group, hence of the spin group. In this paper, we firstly introduce some properties for homogeneous polynomial null solutions to bosonic Laplacians, which give us some important results, such as an orthogonal decomposition of the space of polynomials in terms of homogeneous polynomial null solutions to bosonic Laplacians, etc. This work helps us to introduce Bergman spaces related to bosonic Laplacians, named as bosonic Bergman spaces, in higher spin spaces. Reproducing kernels for bosonic Bergman spaces in the unit ball and a description of bosonic Bergman projection are given as well. At the end, we investigate bosonic Hardy spaces, which are considered as generalizations of harmonic Hardy spaces. Analogs of some well-known results for harmonic Hardy spaces are provided here. For instance, connections to certain complex Borel measure spaces, growth estimates for functions in the bosonic Hardy spaces, etc.
ER -
DING, Chao, Phuoc Tai NGUYEN a Ryan JOHN. Polynomial null solutions to bosonic Laplacians, bosonic bergman and hardy spaces. \textit{Proceedings of the Edinburgh Mathematical Society}. Cambridge University Press, 2022, roč.~65, č.~4, s.~958-989. ISSN~0013-0915. Dostupné z: https://dx.doi.org/10.1017/S0013091522000426.
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