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Equivalence of multi-norms

The theory of multi-norms was developed by H. G. Dales and M. E. Polyakov in a memoir that was published in Dissertationes Mathematicae. In that memoir, the notion of ’equivalence’ of multi-norms was defined. In the present memoir, we make a systematic study of when various pairs of multi-norms are mutually equivalent. In particular, we study when (p,q)-multi-norms defined on spaces L r ( Ω ) are equivalent, resolving most cases; we have stronger results in the case where r = 2. We also show that the standard...

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