Distributional Dimension of Fractal Sets in Local Fields

The distributional dimension of fractal sets in R~n has been systematically studied byTriebel by virtue of the theory of function spaces.In this paper,we first discuss some importantproperties about the B-type spaces and the F-type spaces on local fields,then we give the definitionof the distributional dimension dimin local fields and study the relations between distributionaldimension and Hausdorff dimension.Moreover,the analysis expression of the Hausdorff dimension isgiven.Lastly,we define the Fourier dimension in local fields,and obtain the relations among all thethree dimensions.