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BMO-scale of distribution on ℝ n

René Erlín Castillo;  Julio C. Ramos Fernández — 2008

Czechoslovak Mathematical Journal

Let S ' be the class of tempered distributions. For f ∈ S ' we denote by J - α f the Bessel potential of f of order α . We prove that if J - α f ∈ B M O , then for any λ ∈ ( 0 , 1 ) , J - α ( f ) λ ∈ B M O , where ( f ) λ = λ - n f ( φ ( λ - 1 · ) ) , φ ∈ S . Also, we give necessary and sufficient conditions in order that the Bessel potential of a tempered distribution of order α > 0 belongs to the V M O space.

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