Wavelets in spaces of harmonic functions

Using Meyer's bases of wavelets [1], we construct orthogonal bases of wavelets in the spaces $h_p$ $(1\leqslant p\leqslant \infty)$ of functions harmonic in the unit disc $|z|<1$ or in the annulus $0<\rho<|z|<1$. The partial sums of the Fourier series with respect to these bases possess approximating properties comparable with the best approximations by trigonometric polynomials.