Abstract
Let \(\varOmega \subset {\mathbb {C}}^n\) be a strictly pseudoconvex Runge domain with \(C^2\)-smooth defining function, \(l\in {\mathbb {N}},\) \(p\in (1,\infty ).\) We prove that a holomorphic function f has derivatives of order l in \(H^p(\varOmega )\) if and only if there is a sequence \(\{P_{2^k}\}\) such that \(P_{2^k}\) is a polynomial of degree \(2^k\) and
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The work is supported by Russian Science Foundation Grant 19-11-00058.
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The work is supported by Russian Science Foundation Grant 19-11-00058.
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Rotkevich, A. Constructive Description of Hardy–Sobolev Spaces on Strictly Pseudoconvex Domains. J Geom Anal 32, 41 (2022). https://doi.org/10.1007/s12220-021-00794-y
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DOI: https://doi.org/10.1007/s12220-021-00794-y
Keywords
- Polynomial approximation
- Hardy–Sobolev spaces
- Strictly pseudoconvex domains
- Pseudoanalytic continuation