Asymptotic Relations for the Distributional Stockwell and Wavelet Transforms

Abelian- and Tauberian-type results characterizing the quasiasymptotic behavior of distributions in $S'_{0}(R)$ 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.