A characterization of potential spaces

Dorronsoro, José R.

doi:10.1090/S0002-9939-1985-0796440-3

A characterization of potential spaces
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by José R. Dorronsoro PDF

Proc. Amer. Math. Soc. 95 (1985), 21-31 Request permission

Abstract:

A mean oscillation characterization, valid for all $\alpha > 0$, of the spaces $L_\alpha ^p$ of Bessel potentials of ${L^p}$ functions is given and is used to relate the known characterizations for $0 < \alpha < 2$ via Marcinkiewicz integrals, due to E. M. Stein, and via vector-valued means of differences, due to R. S. Strichartz.

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