Abstract
AbstractRecently, importance of the Besov space has been acknowledged by analysts studing such subsets with lower dimension than the whole space as fractals in the Euclidean space. On the other hand, by taking an extension K of local field K′, K′ is contained in K as a subset with lower dimension than the whole space K and the present author showed that it can be viewed as a d‐set of K in terms of fractal analysis. In this article, Besov spaces on separable extension of the field of p‐adic numbers and on its d‐set will be consistently introduced. After that, a trace theorem showing a relationship between those Besov spaces will be presented and finally a penetrating stochastic process into K′ will be addressed as an application of the trace theorem.
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