This paper deals with the construction of anisotropic curl-free wavelets on rectangular domain, which satisfies the specific boundary conditions. One begins with the revisit of the work on  from the view of basis transform and then gives the construction on rectangular domain. Next, the stability of the corresponding wavelets in curl-free space and the characterization of Sobolev spaces are studied. Finally, we give a Helmholtz decomposition and the representation of curl and div operators in wavelet coordinates.

wavelets, anisotropic, curl-free, rectangular domain, Helmholtz decomposition.