## Gagliardo-Nirenberg type inequalities on Lorentz, Marcinkiewicz and weak-$L^{\infty }$ spaces

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- by Anh Nguyen Dao, Nguyen Lam and Guozhen Lu PDF
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## Abstract:

We establish the Gagliardo-Nirenberg inequality, Trudinger-Moser inequality and John-Nirenberg inequality using the Lorentz spaces $L^{p,\alpha }$, the Marcinkiewicz space $L^{q,\infty }$ and the weak-$L^{\infty }$ space $W$ introduced by Bennett, DeVore and Sharpley [Ann. of Math. (2) 113 (1981), pp. 601–611]. As consequences, we obtain the Gagliardo-Nirenberg type inequality with weak-$L^{\infty }$ norm and BMO norm, Trudinger-Moser type inequality and John-Nirenberg type estimate with $BMO$ norm and weak-$L^{1}$ norm.## References

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## Additional Information

**Anh Nguyen Dao**- Affiliation: Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam
- MR Author ID: 992575
- Email: daonguyenanh@tdtu.edu.vn
**Nguyen Lam**- Affiliation: School of Science and the Environment Grenfell Campus, Memorial University of Newfoundland, Corner Brook, Newfoundland and Labrador A2H5G4, Canada
- MR Author ID: 796424
- ORCID: 0000-0002-8392-6284
- Email: nlam@grenfell.mun.ca
**Guozhen Lu**- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
- MR Author ID: 322112
- Email: guozhen.lu@uconn.edu
- Received by editor(s): June 13, 2020
- Received by editor(s) in revised form: June 1, 2021
- Published electronically: March 28, 2022
- Additional Notes: The first author was supported by Vietnams National Foundation for Science and Technology Development (NAFOSTED) under Project 101.02-2020.17. The research of the first author was also funded by University of Economics Ho Chi Minh City, Vietnam. The second author was supported by an NSERC Discovery Grant. The third author was supported by the Simons Collaboration grant No. 519099 from the Simons Foundation.

The third author is the corresponding author. - Communicated by: Ariel Barton
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**150**(2022), 2889-2900 - MSC (2020): Primary 42B35, 46E35, 26D10
- DOI: https://doi.org/10.1090/proc/15691
- MathSciNet review: 4428875