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›› 2015, Vol. 32 ›› Issue (4): 433-436.DOI: 10.7523/j.issn.2095-6134.2015.04.001

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The boundedness of the fractional truncation operators

CUI Xiaona1, YAN Dunyan2   

  1. 1. College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, Henan, China;
    2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 101408, China
  • Received:2014-10-21 Revised:2015-01-09 Online:2015-07-15

Abstract: In this paper, we consider the boundedness of two kinds of the truncated operators from Lp to Lr. For any fixed p we can obtain a variational interval of r, and we characterize the relationship between the interval and the fractional operators. We also give an estimate of the upper bound of the norm of the operator.

Key words: singular operator, Minkowski's inequality, Hölder's inequality, Fubini theorem

CLC Number: