Abstract
In this paper, we present some new elements of harmonic analysis related to multivariate continuous shearlet transform introduced earlier in Dahlke et al. (J Fourier Anal Appl 16:340–364, 2010; The continuous shearlet transform in arbitrary space dimensions, Philipps-Universitat Marburg, Marburg, 2008). Thus, some results (Parseval’s formula, inversion formula, etc.) are established. Next, we prove an analogue of Heisenberg’s inequality for shearlet transform. Last, we study shearlet transform on subset of finite measures.
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