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On relatively compact sets in quasi-Banach function spaces


Authors: Weichao Guo and Guoping Zhao
Journal: Proc. Amer. Math. Soc. 148 (2020), 3359-3373
MSC (2010): Primary 46B50, 46E30, 42B35
DOI: https://doi.org/10.1090/proc/14963
Published electronically: March 17, 2020
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Abstract: This paper is devoted to the study of the relatively compact sets in quasi-Banach function spaces, providing an important improvement of the known results. As an application, we take the final step in establishing a relative compactness criteria for function spaces with any weight without any assumption.


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Additional Information

Weichao Guo
Affiliation: School of Science, Jimei University, Xiamen, 361021, People’s Republic of China
Email: weichaoguomath@gmail.com

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/14963
Keywords: Banach function spaces, relatively compact, weight
Received by editor(s): April 6, 2019
Received by editor(s) in revised form: October 31, 2019, and December 2, 2019
Published electronically: March 17, 2020
Additional Notes: Supported by the National Natural Foundation of China (Nos. 11701112, 11601456, 11671414, 11771388) and the Natural Science Foundation of Fujian Province (Nos. 2017J01723, 2018J01430).
The second author is the corresponding author
Communicated by: Ariel Barton
Article copyright: © Copyright 2020 American Mathematical Society