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

Abstract:
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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