Abstract
We define a partition of Z into intervals {I j} and prove the Littlewood-Paley inequality ‖f‖ p ≦C p‖Sf‖ p , 2≦p<∞. Heref is a function on [o, 2π) and\(Sf = (\sum |\Delta _j |^2 )^{1/2} , \hat \Delta j = \hat f\chi _{Ij} \). This is a new example of a partition having the Littlewood-Paley property since the {I j} are not of the type obtained by iterating lacunary partitions finitely many times.
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Hare, K.E., Klemes, I. A new type of Littlewood-Paley partition. Ark. Mat. 30, 297–309 (1992). https://doi.org/10.1007/BF02384876
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DOI: https://doi.org/10.1007/BF02384876