A note on continuous fractional wavelet transform in ℝn

Abstract

In this paper, we study the continuous fractional wavelet transform (CFrWT) in [Formula: see text]-dimensional Euclidean space [Formula: see text] with scaling parameter [Formula: see text] such that [Formula: see text]. We obtain inner product relation and reconstruction formula for the CFrWT depending on two wavelets along with the reproducing kernel function, involving two wavelets, for the image space of CFrWT. We obtain Heisenberg’s uncertainty inequality and Local uncertainty inequality for the CFrWT. Finally, we prove the boundedness of CFrWT on the Morrey space [Formula: see text] and estimate [Formula: see text]-distance of the CFrWT of two argument functions with respect to different wavelets.