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MR2184431 (2006h:42039) 42B30 (42B25 46E30)
Kislyakov, S. V.; Parilov, D. V. On the Littlewood-Paley theorem for arbitrary intervals. (Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 327 (2005), Issled. po Linein. Oper. i Teor. Funkts. 33, 98--114, 236--237; translation in J. Math. Sci. (N. Y.) 139 (2006), no. 2, 6417–6424
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