An analogue of the Littlewood–Paley theorem for orthoprojectors onto wavelet subspaces

S. N. Kudryavtsev

Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow

Abstract: 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.

UDC: 517.5

MSC: 42B25, 42C40

Received: 05.04.2015
Revised: 06.07.2015

DOI: 10.4213/im8378

 English version: Izvestiya: Mathematics, 2016, 80:3, 557–601

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