Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 56, pp. 1-4.

Title: Interpolation inequalities between Lorentz space and BMO:
       the endpoint case (L^{1,infinity}, BMO)

Authors: Nguyen Anh Dao (Ton Duc Thang Univ., Ho Chi Minh City, Vietnam)
         Nguyen Thi Ngoc Hanh (Le Loi High school, Gia Lai Province, Vietnam)
         Tran Minh Hieu (Luong The Vinh High school, Gia Lai Province. Vietnam)
         Huy Bac Nguyen (Technical Univ. of Ostrava, Czech Republic)

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 03, 2019.
Math Subject Classifications: 46E35, 26D10.
Key Words: Gagliardo-Nirenberg inequality; Lorentz spaces; BMO space;
           Fractional Sobolev spaces.