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.
Similar content being viewed by others
References
F. John and L. Nirenberg: On functions of bounded mean oscillation. Comm. Pure Appl. Math. 14 (1961), 415–426.
D. Sarason: Functions of bounded mean oscillation. Trans. Amer. Math. Soc. 201 (1975), 391–405.
E. M. Stein: Singular Integrals and Differentiability Properties of Functions. Princenton University Press, Princenton, NJ, 1970.
W. R. Wade: An introduction to Analysis, 2nd ed. Prentice Hall, NJ, 2000.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Castillo, R.E., Ramos Fernández, J.C. BMO-scale of distribution on ℝn . Czech Math J 58, 505–516 (2008). https://doi.org/10.1007/s10587-008-0032-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10587-008-0032-9