On the generalized Hardy's inequality of McGhee, Pigno and Smith and the problem of interpolation between BMO and a Besov space.

Jaak Peetre; Erik Svensson

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Let 1 ≤ p ≤ ∞ and let $w_{0}, w_{1}$ be two weights on the unit circle such that $l o g (w_{0} w_{1}^{- 1}) \in B M O$ . We prove that the couple $(H_{p} (w_{0}), H_{p} (w_{1}))$ of weighted Hardy spaces is a partial retract of $(L_{p} (w_{0}), L_{p} (w_{1}))$ . This completes previous work of the authors. More generally, we have a similar result for finite families of weighted Hardy spaces. We include some applications to interpolation.

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