Characterization of Multiwavelets and MRA Wavelets in Hs(F)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^s(\mathbb {F})$$\end{document}

In the continuation of the paper [Pathak and Singh Wavelet in Sobolev space over local fields of positive characteristic, Int. J. of Wavelets Multi. Inf. Process,16 3 (2018)], we provide the characterizations of multiwavelets in Sobolev space over local fields of positive characteristic (Hs(F))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$( H^s(\mathbb {F}))$$\end{document} by exploiting the theory of affine frame and quasi-affine frame and one example is presented. Further, the wavelets associated with MRA in Hs(F)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ H^s(\mathbb {F})$$\end{document} are also characterized and an example is presented.