Fourier Multipliers and Pseudo-differential Operators on Fock-Sobolev SpacesOperators on Fock-Sobolev SpacesS. Thangavelu

Any bounded linear operator T on L2(Rn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ L^2({\mathbb {R}}^n) $$\end{document} gives rise to the operator S=B∘T∘B∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ S= B \circ T \circ B^*$$\end{document} on the Fock space F(Cn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal {F}({{\mathbb {C}}}^n) $$\end{document} where B is the Bargmann transform. In this article we identify those S which correspond to Fourier multipliers and pseudo-differential operators on L2(Rn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ L^2({\mathbb {R}}^n)$$\end{document} and study their boundedness on the Fock-Sobolev spaces Fs,2(Cn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal {F}^{s,2}({{\mathbb {C}}}^n)$$\end{document}.