Electron. J. Differential Equations, Vol. 2019 (2019), No. 56, pp. 1-4.

Interpolation inequalities between Lorentz space and BMO: the endpoint case $(L^{1,\infty}, BMO)$

Nguyen Anh Dao, Nguyen Thi Ngoc Hanh,Tran Minh Hieu, Huy Bac Nguyen

We prove interpolation inequalities by means of the Lorentz norm, BMO norm, and the fractional Sobolev norm. In particular, we obtain an interpolation inequality for $(L^{1,\infty}, BMO)$, that we call the endpoint case.

Submitted February 6, 2019. Published May 3, 2019.
Math Subject Classifications: 46E35, 26D10.
Key Words: Gagliardo-Nirenberg inequality; Lorentz spaces; BMO space; Fractional Sobolev spaces.

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  Nguyen Anh Dao
Applied Analysis Research Group
Faculty of Mathematics and Statistics
Ton Duc Thang University
Ho Chi Minh City, Vietnam
email: daonguyenanh@tdtu.edu.vn
Nguyen Thi Ngoc Hanh
Le Loi High school
Gia Lai Province, Vietnam
email: nguyenthingochanh.thptleloi@gmail.com
Tran Minh Hieu
Luong The Vinh High school
Gia Lai Province. Vietnam
email: tranhieukbang@gmail.com
Huy Bac Nguyen
Faculty of Electrical Engineering & Computer Science
Technical University of Ostrava
Czech Republic
email: huy.bac.nguyen.st@vsb.cz

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