New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolation. Issue 3 (2006)

• Record Type: Journal Article
• Authors: Pustylnik Pustylnik, Evgeniy Evgeniy; Signes Signes, Teresa Teresa
• Other Names: Cobos Cobos Fernando Fernando Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 4:Issue 3(2006)
• Page Start: 275
• Page End: 304
• Publication Date: 2006
• Subjects: Ultrasymmetric spaces -- weak type interpolation; Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2006/242615
• Languages: English
• ISSNs: 0972-6802

Abstract

Abstract : We study weak type interpolation for ultrasymmetric spaces Lϕ, E i.e., having the norm ‖ ϕ ( t ) f * ( t ) ‖ E ˜, where ϕ ( t ) is any quasiconcave function and E ˜ is arbitrary rearrangement-invariant space with respect to the measure d t / t . When spaces Lϕ, 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, Aϕ, b, E and Bϕ, b, E, which are described and investigated in detail.