Arkiv för Matematik

Volume 57 (2019)

Number 2

Improved fractional Poincaré type inequalities on John domains

Pages: 285 – 315



María Eugenia Cejas (Departmento de Matemática, Universidad Nacional de La Plata, Argentina)

Irene Drelichman (Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Universidad de Buenos Aires, Argentina)

Javier C. Martínez-Perales (Basque Center for Applied Mathematics, Bilbao, Spain)


We obtain improved fractional Poincaré inequalities in John domains of a metric space $(X, d)$ endowed with a doubling measure $\mu$ under some mild regularity conditions on the measure $\mu$. We also give sufficient conditions on a bounded domain to support fractional Poincaré type inequalities in this setting.

Received 20 February 2019

Received revised 4 July 2019

Accepted 1 August 2019

Published 7 October 2019