The continuous quaternion wavelet transform on distribution spaces: The CQWT on distribution spaces: D. Lhamu et al.

This article provides a revised version of some existing results in the literature for the quaternion Fourier transform (QFT) and quaternion wavelet transforms. The inner-product relation and its consequent formula for the continuous quaternion wavelet transform (CQWT) are derived in L p (R 2 ; H) space under the assumption that the admissible wavelet is complex-valued and has a real QFT. Furthermore, the characterization of quaternion Sobolev spaces H s (R 2 ; H) and W m , p (Ω ; H) , weighted quaternion Sobolev space W k m , p (Ω ; H) and generalized quaternion Sobolev space H w ω (R 2 ; H) , quaternion Besov space by means of the CQWT is presented. The CQWT is analysed within these function and distribution spaces, yielding novel findings regarding continuity and boundedness. [ABSTRACT FROM AUTHOR]