In the current work we studied Hardy type and 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 + was proved by Tidblom in (J. Funct. Anal. 221:482-495, 2005).

This paper is about the pseudo-differential operator on the H-type group, denoted by H. We present the trace formula for the a-Weyl transform. Also, we give the characterization of Hilbert-Schmidt class and trace class pseudo-differential operators on H.

No abstract