A tribute to Pola Harboure: Isoperimetric inequalities and the HMS extrapolation theorem

• Carlos Pérez ^[1] ; Ezequiel Rela ^[2]
  1. [1] Universidad del País Vasco/Euskal Herriko Unibertsitatea

     Universidad del País Vasco/Euskal Herriko Unibertsitatea

     Leioa, España

     
  2. [2] Universidad de Buenos Aires

     Universidad de Buenos Aires

     Argentina

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 66, Nº. 1, 2023, págs. 265-280
• Idioma: inglés
• DOI: 10.33044/revuma.4356
• Enlaces
  • Texto completo (pdf)
• Resumen

  • We give a simpler proof of the Gagliardo estimate with a measure obtained by Franchi, Pérez, and Wheeden [Proc. London Math. Soc. (3) 80 no. 3 (2000), 665–689], and improved by Pérez and Rela [Trans. Amer. Math. Soc. 372 no. 9 (2019), 6087–6133]. This result will be further improved using fractional Poincaré type inequalities with the extra bonus of Bourgain–Brezis–Mironescu as done by Hurri-Syrjänen, Martínez-Perales, Pérez, and Vähäkangas [Internat. Math. Res. Notices (2022), rnac246] with a new argument. This will be used with the HMS extrapolation theorem to get Lp type result.