Local linear sigularities and decay of the continuous shearlet transform

Abstract

We obtain a relationship between local linear singularity of a bivariate function and local decay rates of its continuous shearlet transform. This local linear singularity of a function is modeled by directional Hölder regularities. We then consider the situation where singularity on a line segment in a perpendicular direction is significantly lower than that in the direction along the line in a neighborhood.