On the inequality of Bohr for integrals of functions from Lp(Rn) 2 < p < +∞
Abstract
Let p ∈ (2, +∞), n ≥ 1, S be an open subset of Rn, and Γ(S, p) be a set of all the functions γ ∈ Lp(Rn)spectrum of which belongs to S. If n =1 then S can contain zero and if n > 1 S can intersect coordinatehyperplanes. It is obtained sufficient condition validity of the inequality1111r 1111Et1111γ(τ ) dτ 1111L∞ (Rn)≤ C(n, p, S) γ(τ ) Lp (Rn),where t = (t1,..., tn) ∈ Rn, Et = {τ|τ = (τ1,..., τn) ∈ Rn, τj ∈ [0, tj ], if tj ≥ 0, and τj ∈ [tj, 0], if tj < 0, 1 ≤ j ≤ n}, and the constant C(n, p, S) > 0 does not depend on γ ∈ Γ(S, p). Refs 14.
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.