Real interpolation of weighted tent spaces

Abstract

Let and be a Muckenhoupt weight. In this article, the authors study the real interpolation of the weighted tent space . For all , , and , the authors show that , where and denotes the weighted Lorentz-tent space, which is introduced in this article. As an application, the authors prove a real interpolation result on the weighted Hardy spaces for all and , which, when , seals a gap existing in the original proof of a corresponding result of Fefferman et al. [Trans. Amer. Math. Soc. 1974;191:75–81].

Keywords:

• Real interpolation
• tent space
• Lorentz space
• Hardy space
• Muckenhoupt weight
• decreasing rearrangement
• Hardy inequality

AMS Subject Classifications:

• Primary: 46B70
• Secondary: 42B35
• 42B30
• 46E30

Additional information

Funding

Jun Cao is supported by the National Natural Science Foundation of China [grant number 11501506]; the Natural Science Foundation of Zhejiang University of Technology [grant number 2014XZ011]. Der-Chen Chang is supported by the NSF of USA [grant number DMS-1203845]; Hong Kong RGC competitive earmarked research [grant number 601813], [grant number 601410]. Zunwei Fu is supported by the National Natural Science Foundation of China [grant number 11271175]. Dachun Yang is supported by the National Natural Science Foundation of China [grant number 11571039], [grant number 11361020]; the Specialized Research Fund for the Doctoral Program of Higher Education of China [grant number 20120003110003]; the Fundamental Research Funds for Central Universities of China [grant number 2013YB60], [grant number 2014KJJCA10].