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Estimation of the position of intermediate spaces for a Banach couple

Evgenii Pustylnik (1993)

Studia Mathematica

The position of intermediate spaces for a Banach couple is estimated with the help of its fundamental function and co-function. We study the completeness of the collection of all such functions, and the methods of calculating and estimating them for different couples. Finally, these functions are used to compare the position of spaces obtained under the action of some interpolation functors.

Extrapolation of Sobolev imbeddings.

M. Krbec (1997)

Collectanea Mathematica

We survey recent results on limiting imbeddings [sic] of Sobolev spaces, particularly, those concerning weakening of assumptions on integrability of derivatives, considering spaces with dominating mixed derivatives and the case of weighted spaces.

Extrapolation theory for the real interpolation method.

María J. Carro, Joaquim Martín (2002)

Collectanea Mathematica

We develop an abstract extrapolation theory for the real interpolation method that covers and improves the most recent versions of the celebrated theorems of Yano and Zygmund. As a consequence of our method, we give new endpoint estimates of the embedding Sobolev theorem for an arbitrary domain Omega.

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