BMO-scale of distribution on ?
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Authors: | René Erlín Castillo Julio C Ramos Fernández |
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Institution: | (1) Castillo Department of Mathematics, Ohio University, Athens, Ohio 45701, USA;(2) Departamento de Matemáticas, Universidad de Oriente, 6101 Cumaná, Edo. Sucre, Venezuela |
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Abstract: | Let S′ be the class of tempered distributions. For ƒ ∈ S′ we denote by J
−α
ƒ the Bessel potential of ƒ of order α. We prove that if J
−α
ƒ ∈ BMO, then for any λ ∈ (0, 1), J
−α
(f)λ ∈ BMO, 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 VMO space. |
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Keywords: | BMO VMO John and Niereberg Bessel potential |
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