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Sharp weighted convolution inequalities and some applications

Volume 241 / 2018

Weichao Guo, Dashan Fan, Huoxiong Wu, Guoping Zhao Studia Mathematica 241 (2018), 201-239 MSC: Primary 42B15; Secondary 42B35. DOI: 10.4064/sm8583-5-2017 Published online: 10 November 2017


The index groups for which weighted Young inequalities hold in both the continuous case and discrete case are characterized. As applications, the index groups for the product inequalities on modulation spaces are characterized, and we also obtain the weakest conditions for the boundedness of bilinear Fourier multipliers on modulation spaces. For the fractional integral operator, sharp conditions for the power weighted $L^p\text {-}L^q$ estimates in both the continuous and discrete cases are obtained. By a novel unified approach, we complete some previous results on sharp conditions for some classical inequalities.


  • Weichao GuoSchool of Mathematics and Information Sciences
    Guangzhou University
    Guangzhou, 510006, P.R. China
  • Dashan FanDepartment of Mathematics
    University of Wisconsin-Milwaukee
    Milwaukee, WI 53201, U.S.A.
  • Huoxiong WuSchool of Mathematical Sciences
    Xiamen University
    Xiamen, 361005, P.R. China
  • Guoping ZhaoSchool of Applied Mathematics
    Xiamen University of Technology
    Xiamen, 361024, P.R. China

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