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Inclusion relations between modulation and Triebel-Lizorkin spaces


Authors: Weichao Guo, Huoxiong Wu and Guoping Zhao
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 46E35, 42B35
DOI: https://doi.org/10.1090/proc/13614
Published electronically: May 30, 2017
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Abstract: In this paper, we obtain the sharp conditions of the inclusion relations between modulation spaces $ M_{p,q}^s$ and Triebel-Lizorkin spaces $ F_{p,r}$ for $ p\leq 1$, which greatly improve and extend the results for the embedding relations between local Hardy spaces and modulation spaces obtained by Kobayashi, Miyachi and Tomita in [Studia Math. 192 (2009), 79-96].


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Additional Information

Weichao Guo
Affiliation: School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, People’s Republic of China
Email: weichaoguomath@gmail.com

Huoxiong Wu
Affiliation: School of Mathematical Sciences, Xiamen University, Xiamen, 361005, People’s Republic of China
Email: huoxwu@xmu.edu.cn

Guoping Zhao
Affiliation: School of Applied Mathematics, Xiamen University of Technology, Xiamen, 361024, People’s Republic of China
Email: guopingzhaomath@gmail.com

DOI: https://doi.org/10.1090/proc/13614
Keywords: Triebel-Lizorkin spaces, modulation spaces, inclusion relation
Received by editor(s): July 30, 2016
Received by editor(s) in revised form: December 8, 2016
Published electronically: May 30, 2017
Additional Notes: This work was partly supported by the NNSF of China (Grant Nos. 11371295, 11471041, 11601456) and the NSF of Fujian Province of China (No. 2015J01025).
Communicated by: Svitlana Mayboroda
Article copyright: © Copyright 2017 American Mathematical Society