Multiwavelets in the generalized Sobolev space HWω(Rn)

A class of rr-regular multiwavelets is introduced with appropriate notation and definitions in HWω(Rn). The oscillation properity of the orthonormal system is obtained. A multiresolution analysis for multiwavelets is defined in HWω(Rn). Orthonormality conditions for multiscaling functions and multiwavelets are obtained. A multiwavelet expansion formula of Riesz potentials is given.