Extrapolation of operators acting into quasi-Banach spaces. (11th March 2016)

• Record Type: Journal Article
• Authors: Lykov, K V
• Is Part Of: Sbornik. Volume 207:Number 1(2016)
• Page Start: 85
• Page End: 112
• Publication Date: 2016-03-11
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1070/SM8441
• Languages: English
• ISSNs: 1064-5616

Abstract

Abstract: Linear and sublinear operators acting from the scale of$ L_p$ spaces to a certain fixed quasinormed space are considered. It is shown how the extrapolation construction proposed by Jawerth and Milman at the end of 1980s can be used to extend a bounded action of an operator from the$ L_p$ scale to wider spaces. Theorems are proved which generalize Yano's extrapolation theorem to the case of a quasinormed target space. More precise results are obtained under additional conditions on the quasinorm. Bibliography: 35 titles.