Abstract
We investigate the weighted boundedness for a class of local lacunary maximal operators on arbitrary homogeneous Lie groups. On Rn, we analyse the Lp-Lq-boundedness for a class of local lacunary maximal functions on weighted spaces. Our analysis covers weighted dyadic maximal functions as the following ones: (Formula presented.) and also dyadic maximal operators of the form (Formula presented.) where dσ denotes the normalised surface measure on the sphere Sn-1⊂Rn. We also consider the weighted boundedness for a class of local lacunary maximal functions on homogeneous Lie groups, and we present applications of our results on the Heisenberg group for weighted local lacunary maximal functions defined by spherical averages associated with the Korányi sphere.
| Original language | English |
|---|---|
| Pages (from-to) | 926-943 |
| Number of pages | 18 |
| Journal | Journal of Mathematical Sciences (United States) |
| Volume | 289 |
| Issue number | 6 |
| DOIs | |
| State | Published - Apr 2025 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.
Keywords
- Homogeneous Lie groups
- Lacunary maximal function
- Maximal function
- Spherical averages
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics
- Applied Mathematics
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