TY - JOUR
T1 - Generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on domains
AU - Izuki, Mitsuo
AU - Noi, Takahiro
N1 - Funding Information:
The authors are thankful to reviewers for their careful reading of this paper and their comments. The first author was partially supported by Grand-in-Aid for Scientific Research (C), No. 15K04928, for Japan Society for the Promotion of Science. The second author was partially supported by Grand-in-Aid for Young Scientists (B), No. 17K14207, for Japan Society for the Promotion of Science.
Funding Information:
The authors are thankful to reviewers for their careful reading of this paper and their comments. The first author was partially supported by Grand‐in‐Aid for Scientific Research (C), No. 15K04928, for Japan Society for the Promotion of Science. The second author was partially supported by Grand‐in‐Aid for Young Scientists (B), No. 17K14207, for Japan Society for the Promotion of Science.
Publisher Copyright:
© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
PY - 2019/10/1
Y1 - 2019/10/1
N2 - 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.
AB - 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.
KW - Besov space
KW - Morrey space
KW - Primary: 42B35; Secondary: 41A17
KW - Triebel–Lizorkin space
KW - non-smooth atomic decomposition
KW - trace operator
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U2 - 10.1002/mana.201700357
DO - 10.1002/mana.201700357
M3 - Article
AN - SCOPUS:85071041497
SN - 0025-584X
VL - 292
SP - 2212
EP - 2251
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
IS - 10
ER -