ABSTRACT
Accordingly, it is natural to consider spaces in which the norm locally (near the conical point) possesses a similar invariance property:
‖λγg∗λu‖ = ‖u‖ , (2.4) where γ ∈ R is a given number. THEOREM 2.1. Let s, γ ∈ R be given numbers. Then, up to norm equivalence, there exists a unique Hilbert function space H on M◦ satisfying the following conditions:
(i) The norm in H is equivalent to the ordinary Sobolev norm of order s on functions supported in the set {r ≥ ε} ⊂ M◦, where ε > 0 is arbitrary.
