Theorems of Littlewood--Paley type for multiple Fourier integrals
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Investigations in the theory of differentiable functions of many variables and its applications. Part 2, Tome 89 (1967), pp. 214-230.

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@article{TM_1967_89_a10,
     author = {P. I. Lizorkin},
     title = {Theorems of {Littlewood--Paley} type for multiple {Fourier} integrals},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {214--230},
     publisher = {mathdoc},
     volume = {89},
     year = {1967},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_1967_89_a10/}
}
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P. I. Lizorkin. Theorems of Littlewood--Paley type for multiple Fourier integrals. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Investigations in the theory of differentiable functions of many variables and its applications. Part 2, Tome 89 (1967), pp. 214-230. http://geodesic.mathdoc.fr/item/TM_1967_89_a10/