The supremum-involving Hardy-type operators on Lorentz-type spaces
Qinxiu Sun
Zhejiang University of Science and Technology, Hangzhou, ChinaXiao Yu
Shangrao Normal University, ChinaHongliang Li
Zhejiang International Studies University, Hangzhou, China
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Abstract
Given measurable functions on an interval and a kernel function on satisfying Oinarov condition, the supremum-involving Hardy-type operators
in Orlicz-Lorentz spaces are investigated. We obtain sufficient conditions of boundedness of and . Furthermore, in the case of weighted Lorentz spaces, two characterizations of the boundedness of the operator are achieved as well as the compactness of the operator is characterized. It is notable that in the present paper the spaces are only required to be quasi-Banach spaces other than Banach spaces.
Cite this article
Qinxiu Sun, Xiao Yu, Hongliang Li, The supremum-involving Hardy-type operators on Lorentz-type spaces. Port. Math. 77 (2020), no. 1, pp. 1–29
DOI 10.4171/PM/2042