Geodesic
Wavelets in spaces of harmonic functions
Izvestiya. Mathematics , Tome 64 (2000) no. 1, pp. 143-171

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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. 
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     author = {Yu. N. Subbotin and N. I. Chernykh},
     title = {Wavelets in spaces of harmonic functions},
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Yu. N. Subbotin; N. I. Chernykh. Wavelets in spaces of harmonic functions. Izvestiya. Mathematics , Tome 64 (2000) no. 1, pp. 143-171. http://geodesic.mathdoc.fr/item/IM2_2000_64_1_a4/