Asymptotic relations for the distributional Stockwell and wavelet transforms

Abelian- and Tauberian-type results characterizing the quasiasymptotic behavior of distributions in $\mathcal{S}_{0}'(\mathbb{R})$ in terms of their Stockwell transforms are obtained. An Abelian-type result relating the quasiasymptotic boundedness of Lizorkin distributions to the asymptotic behavior of their Stockwell transforms is given. Several asymptotic results for the distributional wavelet transform are also presented.