On generalized inequalities for nonuniform wavelet frames in L2(K)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2({\mathbb {K}})$$\end{document}

Wavelet frames are different from the orthonormal wavelets because of redundancy. By sacrificing orthonormality and allowing redundancy, wavelet frames become much easier to construct than the orthonormal wavelets. An important problem in practice is therefore to determine conditions on the wavelet function, dilation and translation parameters so that the corresponding wavelet system forms a frame. In this paper, we establish some inequalities for nonuniform wavelet system to be frame in L2(K)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2({\mathbb {K}})$$\end{document}. Our results are improved than the known ones by Bhat (Int J Wavelets Multiresol Inf Process 16(1):1850005, 2018) and Li and Jiang (J Math Anal Appl 345:500–510, 2008).