Journal of Function Spaces (Jan 2020)

Sharp Bounds for Fractional Conjugate Hardy Operator on Higher-Dimensional Product Spaces

  • Zequn Wang,
  • Mingquan Wei,
  • Qianjun He,
  • Dunyan Yan

DOI
https://doi.org/10.1155/2020/5064156
Journal volume & issue
Vol. 2020

Abstract

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In this paper, we obtain the sharp bound for fractional conjugate Hardy operator on higher-dimensional product spaces from L1ℝn1×⋯×ℝnm to the space wLQℝn1×⋯×ℝnm and Lpℝn1×⋯×ℝnm to the space Lqℝn1×⋯×ℝnm. More generally, the operator norm of the fractional Hardy operator on higher-dimensional product spaces from LPℝn1×⋯×ℝnm to LQIℝn1×⋯×ℝnm is obtained.