TY - JOUR
T1 - On the extension of Muckenhoupt weights in metric spaces
AU - Kurki, Emma Karoliina
AU - Mudarra, Carlos
N1 - Funding Information:
Acknowledgments. E.-K. Kurki was funded by a young researcher’s grant from the Emil Aaltonen Foundation, Finland . C. Mudarra acknowledges financial support from the Academy of Finland . We thank Juha Kinnunen for many helpful discussions.
Publisher Copyright:
© 2021 The Author(s)
PY - 2022/2
Y1 - 2022/2
N2 - A theorem by Wolff states that weights defined on a measurable subset of Rn and satisfying a Muckenhoupt-type condition can be extended into the whole space as Muckenhoupt weights of the same class. We give a complete and self-contained proof of this theorem generalized into metric measure spaces supporting a doubling measure. Related to the extension problem, we also show estimates for Muckenhoupt weights on Whitney chains in the metric setting.
AB - A theorem by Wolff states that weights defined on a measurable subset of Rn and satisfying a Muckenhoupt-type condition can be extended into the whole space as Muckenhoupt weights of the same class. We give a complete and self-contained proof of this theorem generalized into metric measure spaces supporting a doubling measure. Related to the extension problem, we also show estimates for Muckenhoupt weights on Whitney chains in the metric setting.
KW - Doubling condition
KW - Metric measure space
KW - Muckenhoupt weight
UR - http://www.scopus.com/inward/record.url?scp=85119082140&partnerID=8YFLogxK
U2 - 10.1016/j.na.2021.112671
DO - 10.1016/j.na.2021.112671
M3 - Article
AN - SCOPUS:85119082140
VL - 215
JO - NONLINEAR ANALYSIS: THEORY METHODS AND APPLICATIONS
JF - NONLINEAR ANALYSIS: THEORY METHODS AND APPLICATIONS
SN - 0362-546X
M1 - 112671
ER -