The n-dimensional continuous wavelet transformation on Gelfand and Shilov type spaces

In this paper the wavelet transformationon Gelfand and Shilov spaces of type WM( n), WΩ(Δn) and WMΩ(Δn) is studied. It is shown that Wψφ : WM( n) → WM( n× +n), Wψφ : WΩ(Δn) →WΩ(Δn× +n) and Wψφ : WMΩ(Δn) →WMΩ(Δn× +n) is linear andcontinuous where n and Δn are n-dimensional realnumbers and complex numbers. A boundedness result in a generalized Sobolev space is derived.