Generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on domains

Mitsuo Izuki and Takahiro Noi

Mathematische Nachrichten, 2019, vol. 292, issue 10, 2212-2251

Abstract: In this paper, we consider a non‐smooth atomic decomposition by using a smooth atomic decomposition. Applying the non‐smooth atomic decomposition, a local means characterization and a quarkonical decomposition, we obtain a pointwise multiplier and a trace operator for generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on the whole space. We also develop the theory of those spaces on domains. We consider an extension operator and a trace operator on the upper half space and on compact oriented Riemannian manifolds.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:292:y:2019:i:10:p:2212-2251

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