Publisher： Cambridge University Press
E-ISSN： 1755-1633|21|2|189-205
ISSN： 0004-9727
Source： Bulletin of the Australian Mathematical Society, Vol.21, Iss.2, 1980-05, pp. : 189-205
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Abstract
Spaces with homogeneous norms are closely related to the Beppo Levi spaces of Deny and Lions, to spaces of Riesz potentials, and to Sobolev spaces. In this paper we survey the literature on them, give a broad extension of their definition, and present their basic theory. Many of the properties of Sobolev spaces have their analogues. In fact, the two families are locally equivalent. Spaces with homogeneous norms are especially suited to the study of boundary value problems on
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