Parabolic Muckenhoupt Weights with Time Lag on Spaces of Homogeneous Type with Monotone Geodesic Property
- Resource Type
- Original Paper
- Authors
- Kinnunen, Juha; Myyryläinen, Kim; Yang, Dachun; Zhu, Chenfeng
- Source
- Potential Analysis: An International Journal Devoted to the Interactions between Potential Theory, Probability Theory, Geometry and Functional Analysis. 60(4):1513-1569
- Subject
- Space of homogeneous type
Parabolic Muckenhoupt weight
Parabolic maximal operator
Parabolic reverse Hölder inequality
Parabolic BMO
Primary: 46E36. Secondary: 42B35
42B25
30L99
- Language
- English
- ISSN
- 0926-2601
1572-929X
This work discusses parabolic Muckenhoupt weights with time lag on spaces of homogeneous type with an extra monotone geodesic property. The main results include a characterization in terms of weighted norm inequalities for parabolic maximal operators, a reverse Hölder inequality, and a Jones-type factorization result for this class of weights. The connection between the space of parabolic bounded mean oscillation and parabolic Muckenhoupt weights is studied by applying a parabolic John–Nirenberg lemma. A Coifman–Rochberg-type characterization of the space of parabolic bounded mean oscillation in terms of parabolic maximal functions is also given. The main challenges in the parabolic theory are related to the time lag in the estimates. The results are motivated by the corresponding Euclidean theory and the regularity theory for parabolic variational problems on metric measure spaces.