In the previous chapter, characterizations of the inversion formula of the continuous Bessel wavelet transform in \(H_\mu ^\prime (I)\) were discussed and found applications in the Heat equation and the Calderón reproducing formula in \(H_\mu ^\prime (I)\) . In this chapter, the inversion formula and its properties are discussed exploiting the theory of the continuous Bessel wavelet transform of distributions on \(\beta _{\mu }^\prime \) -space.