Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615969 | Journal of Mathematical Analysis and Applications | 2014 | 15 Pages |
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 fâLp(R) (1⩽p<â), asΣ(f)=âkâLq(R)spB{fâk}¯(1p+1q=1), where spB{â
} is the Beurling spectrum. It is shown that if ÏâR satisfies the condition 0⩽ÏÏ<Ï, then fâ²âLp(R) andâfâ²âp⩽Ï2sinÏÏâf(â
+Ï)âf(â
âÏ)âp, where Ï:=sup{|λ|:λâΣ(f)}. Some related problems are also discussed.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
H.S. Mustafayev,