TY - JOUR
T1 - A remark on the paper"Vector-valued operators with singular kernel and Triebel-Lizorkin block spaces with variable exponents" by Kwok Pun Ho
AU - Hatano, Naoya
AU - Nogayama, Toru
AU - Sawano, Yoshihiro
N1 - Funding Information:
Acknowledgments. First of all, the authors are grateful to the anonymous referee for his/her careful reading, which increased the readability of the paper. Naoya Hatano was financially supported by a Research Fellowship from the Japan Society for the Promotion of Science for Young Scientists (21J12129). Toru Nogayama was supported financially by a Research Fellowship of the Japan Society for the Promotion of Science for Young Scientists (20J10403). Yoshihiro Sawano was partially supported by a Grant-in-Aid for Scientific Research (C) (No. 19K03546) of the Japan Society for the Promotion of Science as well as the People’s Friendship University of Russia.
Publisher Copyright:
© 2022 by Kyoto University.
PY - 2022/6
Y1 - 2022/6
N2 - Our goal of this paper is to show that Ho's vector-valued Morrey spaces can be realized as a special case of pointwise multiplier spaces. This extends Lemarié- Rieusset's theorem. One cannot extend his theorem directly, because we are handling Banach lattices instead of Lebesgue spaces. It turns out that mixed Morrey spaces, Lorentz-Morrey spaces, and Orlicz-Morrey spaces fall under the scope of the framework in this paper. This work can be located as a continuation of the huge study of multiplier spaces collected in the book of Maz'ya.
AB - Our goal of this paper is to show that Ho's vector-valued Morrey spaces can be realized as a special case of pointwise multiplier spaces. This extends Lemarié- Rieusset's theorem. One cannot extend his theorem directly, because we are handling Banach lattices instead of Lebesgue spaces. It turns out that mixed Morrey spaces, Lorentz-Morrey spaces, and Orlicz-Morrey spaces fall under the scope of the framework in this paper. This work can be located as a continuation of the huge study of multiplier spaces collected in the book of Maz'ya.
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U2 - 10.1215/21562261-2022-0008
DO - 10.1215/21562261-2022-0008
M3 - Article
AN - SCOPUS:85132238804
VL - 62
SP - 357
EP - 375
JO - Journal of Mathematics of Kyoto University
JF - Journal of Mathematics of Kyoto University
SN - 0023-608X
IS - 2
ER -