• Title/Summary/Keyword: symmetric decreasing rearrangement

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FRACTIONAL POLYA-SZEGÖ INEQUALITY

  • Park, Young Ja
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.2
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    • pp.267-271
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    • 2011
  • Let 0 < s < 1. For $f^{\ast}$ representing the symmetric radial decreasing rearrangement of f, we build up a fractional version of Polya-$Szeg{\ddot{o}}$ inequality: $${\int}_{\mathbb{R}^n}{\mid}(-\Delta)^{s/2}f^{\ast}(x){\mid}^2dx{\leq}{\int}_{\mathbb{R}^n}{\mid}(-\Delta)^{s/2}f(x){\mid}^2dx$$.