Article ID Journal Published Year Pages File Type
4615969 Journal of Mathematical Analysis and Applications 2014 15 Pages PDF
Abstract
In 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 Lp-spaces: We define the spectrum Σ(f) of f∈Lp(R) (1⩽p<∞), asΣ(f)=⋃k∈Lq(R)spB{f⁎k}¯(1p+1q=1), where spB{⋅} is the Beurling spectrum. It is shown that if τ∈R satisfies the condition 0⩽τσ<π, then f′∈Lp(R) and‖f′‖p⩽σ2sinτσ‖f(⋅+τ)−f(⋅−τ)‖p, where σ:=sup{|λ|:λ∈Σ(f)}. Some related problems are also discussed.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
Authors
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