$L^p$-estimates for harmonic Bergman projection on a class of convex domains of infinite type in $\mathbb{C}^2$

Ly Kim HA; Nguyen Van Sang HONG

doi:5110ojm

October 2021 $L^p$-estimates for harmonic Bergman projection on a class of convex domains of infinite type in $\mathbb{C}^2$

Ly Kim HA, Nguyen Van Sang HONG

Author Affiliations +

Osaka J. Math. 58(4): 967-981 (October 2021).

Abstract

In this paper, we prove that the Bergman projection extends continuously to a projection from harmonic $L^1$-functions onto holomorphic $L^1$-functions and maps continuously $L^{\infty}$-functions onto the space of Bloch holomorphic functions in a certain class of infinite type, convex domains in $\mathbb{C}^2$.

Funding Statement

This research is funded by Vietnam National University Ho Chi Minh City (VNU-HCM) under grant number B2019-18-01. The paper was completed during a scientific stay of the first author at the Vietnam Institute for Advanced Study in Mathematics (VIASM) 2019, whose hospitality is gratefully appreciated.

Acknowledgments

The authors thank the referees for useful remarks and comments that led to the improvement of the paper.

Citation

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Ly Kim HA. Nguyen Van Sang HONG. "$L^p$-estimates for harmonic Bergman projection on a class of convex domains of infinite type in $\mathbb{C}^2$." Osaka J. Math. 58 (4) 967 - 981, October 2021.