Abstract
We define a partition of Z into intervals {Ij} and prove the Littlewood-Paley inequality ‖f‖p≦Cp‖Sf‖p, 2≦p<∞. Here f 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 {Ij} are not of the type obtained by iterating lacunary partitions finitely many times.
Citation
Kathryn E. Hare. Ivo Klemes. "A new type of Littlewood-Paley partition." Ark. Mat. 30 (1-2) 297 - 309, 1992. https://doi.org/10.1007/BF02384876
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