Journal of Function Spaces

Journal of Function Spaces / 2006 / Article

Open Access

Volume 4 |Article ID 242615 | https://doi.org/10.1155/2006/242615

Evgeniy Pustylnik, Teresa Signes, "New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolation", Journal of Function Spaces, vol. 4, Article ID 242615, 30 pages, 2006. https://doi.org/10.1155/2006/242615

New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolation

Academic Editor: Fernando Cobos
Received01 Dec 2005

Abstract

We study weak type interpolation for ultrasymmetric spaces L?,E i.e., having the norm ??(t)f*(t)?E˜, where ?(t) is any quasiconcave function and E˜ is arbitrary rearrangement-invariant space with respect to the measure dt/t. When spaces L?,E are not “too close” to the endpoint spaces of interpolation (in the sense of Boyd), the optimal interpolation theorem was stated in [13]. The case of “too close” spaces was studied in [15] with results which are optimal, but only among ultrasymmetric spaces. In this paper we find better interpolation results, involving new types of rearrangement-invariant spaces, A?,b,E and B?,b,E, which are described and investigated in detail.

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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