Let $\mathbb{ H}$ be the general, reduced Heisenberg group. Our main result establishes the inverse-closedness of a class of integral operators acting on $L^{ p}(\mathbb{ H})$, given by the off-diagonal decay of the kernel. As a consequence of this result, we show that if $\alpha_{ 1}I+S_{ f}$, where $S_{ f}$ is the operator given by convolution with $f$, $f\in L^{ 1}_{ v}(\mathbb{ H})$, is invertible in $\B(L^{ p}(\mathbb{ H}))$, then (\alpha_{ 1}I+S_{ f})^{ -1}=\alpha_{ 2}I+S_{ g}$, and $g\in L^{ 1}_{ v}(\mathbb{ H})$. We prove analogous results for twisted convolution operators and apply the latter results to a class of Weyl pseudodifferential operators. We briefly discuss relevance to mobile communications.
Categories: math.CA