Wavelet bases on the L-shaped domain

We present in this paper two elementary constructions of multiresolution analyses on the L-shaped domain D . In the first one, we shall describe a direct method to define an orthonormal multiresolution analysis. In the second one, we use the decomposition method for constructing a biorthogonal multiresolution analysis. These analyses are adapted for the study of the Sobolev spaces H s ( D ) ( s ∈ N ) .