Dilation Operators in Besov Spaces over Local Fields

Abstract

We consider a dilation operator on Besov spaces (B s r,t (K)) over local fields and estimate an operator norm on such a field for s > σ r = max( 1 r − 1, 0) which depends on the constant k unlike the case of Euclidean spaces. In R n , it is independent of constant. A constant k appears for liming case s = 0 and s = σ r . In case of local fields, the limig case is still open. Further we also estimate the localization property of Besov spaces over local fields.