Approximation of linear canonical wavelet transform on the generalized Sobolev spaces

The main objective of this paper is to study the linear canonical wavelet transform (LCWT) on generalized Sobolev space Bp,kξ,A(R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B^{\xi ,A}_{p,k}(\mathbb {R})$$\end{document} and generalized weighted space Lϵ,As,p(R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{s,p}_{\epsilon ,A}(\mathbb {R})$$\end{document}. Its approximation properties and convergence of convolution for FψA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F^{A}_{\psi }$$\end{document} in the space Bp,kξ,A(R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B^{\xi ,A}_{p,k}(\mathbb {R})$$\end{document} are also discussed. Based on these properties, we prove that the LCWT is linear continuous mapping on the spaces of Fp,A∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F^{*}_{p,A}$$\end{document} and Up,Ak\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ U^{k}_{p,A}$$\end{document}. The composition of LCWTs is defined and studied some results related to it. Moreover, the boundedness results of LCWT as well as composition of LCWTs on the space Hϵ,As(R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^{s}_{\epsilon ,A}(\mathbb {R})$$\end{document} are studied.