The Kato-ponce Inequality

  title={The Kato-ponce Inequality},
  author={Loukas Grafakos and ‖∇f‖L∞ ∥∥Js−1g},
In this article we revisit the inequalities of Kato and Ponce concerning the L norm of the Bessel potential J = (1 − ∆) (or Riesz potential D = (−∆)) of the product of two functions in terms of the product of the L norm of one function and the L norm of the the Bessel potential J (resp. Riesz potential D) of the other function. Here the indices p, q, and r are related as in Hölder’s inequality 1/p + 1/q = 1/r and they satisfy 1 ≤ p, q ≤ ∞ and 1/2 ≤ r < ∞. Also the estimate is weak-type in the… CONTINUE READING

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