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Generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on domains
Author(s) -
Izuki Mitsuo,
Noi Takahiro
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700357
Subject(s) - mathematics , pointwise , pure mathematics , besov space , trace (psycholinguistics) , multiplier (economics) , mathematical analysis , characterization (materials science) , operator (biology) , space (punctuation) , interpolation space , functional analysis , physics , biochemistry , chemistry , linguistics , philosophy , macroeconomics , optics , repressor , transcription factor , economics , gene
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.