Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898406 | Journal of Approximation Theory | 2018 | 22 Pages |
Abstract
In this paper, we investigate entropy numbers of multiplier operators Î={λk}kâZd and Îâ={λkâ}kâZd, Î,Îâ:Lp(Td)âLq(Td) on the d-dimensional torus Td, where λk=λ(|k|) and λkâ=λ(|k|â) for a function λ defined on the interval [0,â), with |k|=k12+â¯+kd21â2 and |k|â=max1â¤jâ¤d|kj|. In the first part, upper and lower bounds are established for entropy numbers of general multiplier operators. In the second part, we apply these results to the specific multiplier operators Î(1)=|k|âγ(ln|k|)âξkâZd, Îâ(1)=|k|ââγ(ln|k|â)âξkâZd, Î(2)=eâγ|k|rkâZd and Îâ(2)=eâγ|k|ârkâZd for γ>0, 0
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
R.L.B. Stabile, S.A. Tozoni,