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

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 ??(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 interpolatio...

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Main Authors: Evgeniy Pustylnik, Teresa Signes
Format: Article
Language:English
Published: Hindawi Limited 2006-01-01
Series:Journal of Function Spaces and Applications
Online Access:http://dx.doi.org/10.1155/2006/242615
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spelling doaj-64399f58726b4105b8f0e8c2c5023d8f2020-11-25T00:32:42ZengHindawi LimitedJournal of Function Spaces and Applications0972-68022006-01-014327530410.1155/2006/242615New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolationEvgeniy Pustylnik0Teresa Signes1Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, IsraelDepartamento de Matemática Aplicada, Facultad de Informática, Universidad de Murcia, Campus de Espinardo, 30100 Espinardo (Murcia), SpainWe 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.http://dx.doi.org/10.1155/2006/242615
collection DOAJ
language English
format Article
sources DOAJ
author Evgeniy Pustylnik
Teresa Signes
spellingShingle Evgeniy Pustylnik
Teresa Signes
New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolation
Journal of Function Spaces and Applications
author_facet Evgeniy Pustylnik
Teresa Signes
author_sort Evgeniy Pustylnik
title New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolation
title_short New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolation
title_full New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolation
title_fullStr New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolation
title_full_unstemmed New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolation
title_sort new classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolation
publisher Hindawi Limited
series Journal of Function Spaces and Applications
issn 0972-6802
publishDate 2006-01-01
description 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.
url http://dx.doi.org/10.1155/2006/242615
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AT teresasignes newclassesofrearrangementinvariantspacesappearinginextremecasesofweakinterpolation
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