University of MaraghehSahand Communications in Mathematical Analysis2322-5807Articles in Press20190424$p$-adic Dual Shearlet Frames3496510.22130/scma.2018.77684.355ENMahdieh FatemidokhtDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.Ataollah Askari HemmatDepartment of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.Journal Article20171221We introduced the continuous and discrete $p$-adic shearlet systems. We restrict ourselves to a brief description of the $p$-adic theory and shearlets in real case. Using the group $G_p$ consist of all $p$-adic numbers that all of its elements have a square root, we defined the continuous $p$-adic shearlet system associated with $L^2left(Q_p^{2}right)$. The discrete $p$-adic shearlet frames for $L^2left(Q_p^{2}right)$ is discussed. Also we prove that the frame operator $S$ associated with the group $G_p$ of all with the shearlet frame $SHleft( psi; Lambdaright)$ is a Fourier multiplier with a function in terms of $widehat{psi}$. For a measurable subset $H subset Q_p^{2}$, we considered a subspace $L^2left(Hright)^{vee}$ of $L^2left(Q_p^{2}right)$. Finally we give a necessary condition for two functions in $L^2left(Q_p^{2}right)$ to generate a p-adic dual shearlet tight frame via admissibility.