In this paper, we prove the fractional logarithmic Sobolev inequality on homogeneous groups. Also, we establish fractional logarithmic Gagliardo–Nirenberg and Caffarelli–Kohn–Nirenberg inequalities on homogeneous groups. In addition, we show blow-up results for the fractional heat equation with logarithmic nonlinearity on homogeneous groups.
- Fractional logarithmic Caffarelli–Kohn–Nirenberg inequality
- Fractional logarithmic Gagliardo–Nirenberg inequality
- Fractional logarithmic Sobolev inequality
- Homogeneous group
ASJC Scopus subject areas
- Applied Mathematics