Geodesic
An analogue of the Littlewood–Paley theorem for orthoprojectors onto wavelet subspaces
Izvestiya. Mathematics, Tome 80 (2016) no. 3, pp. 557-601

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We prove an analogue of the Littlewood–Paley theorem for orthoprojectors onto wavelet subspaces corresponding to a non-isotropic multiresolution analysis generated by the tensor product of smooth scaling functions of one variable with sufficiently rapid decay at infinity.
Keywords: orthoprojector, wavelet subspaces, scaling function, multiresolution analysis, Littlewood–Paley theorem. 
S. N. Kudryavtsev. An analogue of the Littlewood–Paley theorem for orthoprojectors onto wavelet subspaces. Izvestiya. Mathematics, Tome 80 (2016) no. 3, pp. 557-601. http://geodesic.mathdoc.fr/item/IM2_2016_80_3_a6/
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