A new wavelet-like transform associated with the Riesz-Bochner integral and relevant reproducing formula

We introduce a new family of wavelet-like transforms associated to the Riesz-Bochner integral of L (p) functions and prove the corresponding reproducing formula of Caldern's type. Unlike the classical wavelet transforms, this is a class of wavelet-like transforms generated by three components, namely, a kernel function (the Riesz-Bochner integral), a weight function and a wavelet function. The first component depends on many variables, but the second and third ones, which are in our disposal, depend only on one variable and therefore give extra simplicity in applications.