On a Problem of Pichorides
Let S(Λ) denote the classical Littlewood–Paley operator formed with respect to a lacunary sequence Λ of positive integers. Motivated by a remark of Pichorides, we obtain sharp asymptotic estimates of the behaviour of the operator norm of S(Λ) from the analytic Hardy space HAp(T) to Lp(T) and of the behaviour of the Lp(T) → Lp(T) operator norm of S(Λ) (1 < p< 2) in terms of the ratio of the lacunar
