Abelian- and Tauberian-type results for the generalized Stockwell and wavelet transforms

Tauberian-type results characterizing the quasiasymptotic behavior of polynomial multiplication of Lizorkin distributions in terms of their Stockwell transform are obtained. Some Abelian-type results relating the quasiasymptotic behavior and quasiasymptotic boundedness of Lizorkin distributions to the asymptotic behavior of their Stockwell transform are given. Several Abelian-type results for the generalized wavelet transform are also presented.