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An approximation theorem for Hardy functions on $\mathbb {C}$-linearly convex domains of infinite type in $\mathbb {C}^2$

Volume 161 / 2020

Ly Kim Ha Colloquium Mathematicum 161 (2020), 223-238 MSC: Primary 32A26; Secondary 32T25, 32A40. DOI: 10.4064/cm7807-5-2019 Published online: 28 March 2020


Let $\Omega \subset \mathbb {C}^2$ be a smoothly bounded, $\mathbb {C}$-linearly convex domain. We prove that if $\Omega $ is of $F$-type at all boundary points (for some type function $F$), then for all $1\le p \lt \infty $, every Hardy function $f\in H^p(\Omega )$ is approximated by a sequence of holomorphic functions on $\overline {\Omega }$ in the $H^p$-norm.


  • Ly Kim HaFaculty of Mathematics and Computer Science
    University of Science
    Vietnam National University Ho Chi Minh City (VNU-HCM)
    227 Nguyen Van Cu street, District 5
    Ho Chi Minh City, Vietnam

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