Mustafayev, H. S.2025-05-102025-05-1020140022-247X1096-081310.1016/j.jmaa.2013.10.0312-s2.0-84887827994https://doi.org/10.1016/j.jmaa.2013.10.031https://hdl.handle.net/20.500.14720/16458In this article, we present inequalities related to the continuous representations of one-parameter groups. As an application, we obtain some differential inequalities of Bernstein type in L-p-spaces: We define the spectrum Sigma(f) of f is an element of L-p (R) (1 <= p < infinity), as Sigma(f) = boolean OR sp(B) {f * k} (1/P + 1/Q = 1), k is an element of L-q (R) where sp(B){.} is the Beurling spectrum. It is shown that if tau is an element of R satisfies the condition 0 <= tau sigma < pi, then f' is an element of L-p(R) and parallel to f'parallel to(p) <= sigma/2 sin tau sigma parallel to f(. + tau) - f(. - tau)parallel to(p), where sigma := sup{vertical bar lambda vertical bar: lambda is an element of Sigma(f)}. Some related problems are also discussed. (C) 2013 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/openAccessCo-GroupLocal SpectrumL-P-SpaceInequalityArticle4112Q2Q2887901WOS:000327569600034