L p $L^{p}$ Hardy type inequality in the half-space on the H-type group

Abstract

Abstract In the current work we studied Hardy type and L p $L^{p}$ Hardy type inequalities in the half-space on the H-type group, where the Hardy inequality in the upper half-space R + n $\mathbf{R}_{+}^{n}$ was proved by Tidblom in (J. Funct. Anal. 221:482-495, 2005).

Keywords

• H-type group
• Hardy type inequality
• Green’s function