Littlewood - Paley theorem on L^p(t)(R^n) spaces - Kopaliani, T. S. (Ukrains’kyi Matematychnyi Zhurnal, 2008)
We point out that when the Hardy - Littlewood maximal operator is bounded on the space L^p(t)(R^n),1 < a ≤ p(t) ≤ b < ∞,t R, the well-known characterization of spaces L^p(t)(R^n),1 < p < ∞, by the Littlewood - Paley theory extends to the space L^p(t)(R^n). We show that if n > 1, the Littlewood -Paley operator is bounded on L^p(t)(R^n),1 < a ≤ p(t) ≤ b < ∞,t R, if and only if p(t) = const.