Fractional Stockwell transform of Lizorkin distributions.

We prove the continuity of the fractional Stockwell transform and the corresponding synthesis operator on the spaces of highly localized functions over $ \mathbb {R} $ R and $ \mathbb {R}\times \mathbb {R}\setminus \{0\} $ R × R ∖ { 0 } , respectively, and their duals. We also provide Abelian and Tauberian-type results relate the asymptotic behaviour of distributions with the asymptotics of their fractional Stockwell transform. [ABSTRACT FROM AUTHOR]