CHAINS OF FUNCTION SPACES OVER EUCLIDIAN SPACES AND LOCAL FIELDS

摘要

The Lipschitz class Lip(K, α) on a local field K is defined in [10], and an equivalent relationship between the Ho¨lder type space Cα(K)[9] and Lip(K,α) is given. In this note, we give a "chain of function spaces" over Euclidian space by defining higher order continuous modulus in R, and point out that there is no need of higher order continuous modulus for describing the chain of function spaces over local fields.