Sharpness of the Brascamp–Lieb inequality in Lorentz spaces

@inproceedings{Bez2017SharpnessOT,
  title={Sharpness of the Brascamp–Lieb inequality in Lorentz spaces},
  author={N. Bez and Sanghyuk Lee and Shohei Nakamura and Yoshihiro Sawano},
  year={2017}
}
We provide necessary conditions for the refined version of the Brascamp-Lieb inequality where the input functions are allowed to belong to Lorentz spaces, thereby establishing the sharpness of the range of Lorentz exponents in the subcritical case. Using similar considerations, some sharp refinements of the Strichartz estimates for the kinetic transport equation are established.