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
We study weak type interpolation for ultrasymmetric spaces L?,E i.e., having the norm , where is any quasiconcave function and is arbitrary rearrangement-invariant space with respect to the measure . 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 . The case of “too close” spaces was studied in  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.
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