Abstract
We obtain sharp weighted Moser-Trudinger inequalities for first-layer symmetric functions on groups of Heisenberg type, and for x-symmetric functions on the Grushin plane. To this end, we establish weighted Young's inequalities in the form ||K*W L||r,W ≤ ||K|| p,W||L||q,W, 1 + 1/r = 1/p + 1/q, for first-layer radial weights W on a general Carnot group script G sign and functions K, L:script G sign → ℝ with L first-layer symmetric. The proofs use some sharp estimates for hypergeometric functions.
Original language | English (US) |
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Pages (from-to) | 357-384 |
Number of pages | 28 |
Journal | Potential Analysis |
Volume | 24 |
Issue number | 4 |
DOIs | |
State | Published - Jun 2006 |
Keywords
- Carnot group
- Grushin plane
- Moser-Trudinger inequality
- Nonlinear potential theory
- Young's inequality
ASJC Scopus subject areas
- Analysis