One-sided Littlewood–Paley inequality in for 0 < p ≤ 2

The one-sided Littlewood–Paley inequality for arbitrary collections of mutually disjoint rectangular parallelepipeds in for the L p -metric, 0 < p ≤ 2, is proved. The paper supplements author’s earlier work, which dealt with the situation of n = 2. That work was based on R . Fefferman’s theory, which makes it possible to verify the boundedness of certain linear operators on two-parameter Hardy spaces (i.e., Hardy spaces on the product of two Euclidean spaces, ). However, Fefferman’s results are not applicable in the situation where the number of Euclidean factors is greater than 2. Here we employ the more complicated Carbery–Seeger theory, which is a further development of Fefferman’s ideas. This allows us to verify the boundedness of some singular integral operators on the multiparameter Hardy spaces , which leads eventually to the required inequality of Littlewood–Paley type. Bibliography: 13 titles.