We give a new proof of Hardy and Littlewood theorem concerning harmonic conjugates of functions u such that ∫D |u(z)|pdA(z) < ∞, 0 < p ≤ 1. We also obtain an inequality for integral means of such harmonic functions u.
In this paper we obtain a condition for analytic square integrable functions which guarantees the boundedness of products of the Toeplitz operators densely defined on the Bergman space in the polydisk. An analogous condition for the products of the Hankel operators is also given.
We give new characterizations of the analytic Besov spaces Bp on the unit ball B of Cn in terms of oscillations and integral means over some Euclidian balls contained in B.
We prove a sufficient condition for products of Toeplitz operators , where f,g are square integrable holomorphic functions in the unit ball in ℂⁿ, to be bounded on the weighted Bergman space. This condition slightly improves the result obtained by K. Stroethoff and D. Zheng. The analogous condition for boundedness of products of Hankel operators is also given.
We give new characterizations of the analytic Besov spaces on the unit ball of in terms of oscillations and integral means over some Euclidian balls contained in .
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