Abstract
Suppose that m ≥ 2, numbers p 1, …, p m ∈ (1, +∞] satisfy the inequality \(\frac{1}{{{p_1}}} + \cdots + \frac{1}{{{p_m}}} 0 is independent of the functions \(\Delta {\gamma _k} \in L_{ak}^{pk}\left( {{ℝ^1}} \right)\) and \(L_{ak}^{pk}\left( {{ℝ^1}} \right) \subset {L^{pk}}\left( {{ℝ^1}} \right)\) , 1 ≤ k ≤ m, are special normed spaces. A condition for the integral over ℝ1 of a product of functions to be bounded is also given.
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