We consider three different spherical means on a Heisenberg type group. First, the standard spherical means, which is the average of a function over the spheres in the complement of the center of the group, second is the average over product of spheres in the center and its complement and the third one over spheres defined by a homogeneous norm on the group. We establish injectivity results for these means on $L^p$ spaces for the range $1 \leq p \leq 2m/(m-1)$ where $m$ is the dimension of the center. Our results extend and generalize S. Thangaveluâ€™s results for spherical means on the Heisenberg group. (Joint work with P. K. Sanjay and K. T. Yasser)

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Last updated: 25 Jan 2023