Abstract
The n-dimensional generalized Hartogs triangles are domains defined by
with
and
. In this paper, we first obtain an estimate for the Bergman kernel of
and then use it to establish the
boundedness of the associated Bergman projections. Our result generalizes the
boundedness result for two-dimensional generalized Hartogs triangles obtained by L.D. Edholm and J.D. McNeal in [Bergman subspaces and subkernels: degenerate Lp mapping and zeroes. J Geom Anal. 2017;27:2658–2683] to n-dimensional settings.
Acknowledgements
The author thanks his Ph.D. advisor Prof. Feng Rong for helpful comments and suggestions to this manuscript. The author also wishes to thank the anonymous referee for their useful comments.
Disclosure statement
No potential conflict of interest was reported by the author(s).