Fundamental solution for the Q-Laplacian and sharp Moser–Trudinger inequality in Carnot groups

By Zoltán M. Balogh, Juan J. Manfredi, Jeremy T. Tyson. 2003

51 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/aa819c44f70763576f55b2abdb9e553d7dabe939

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Moser-Trudinger and Beckner-Onofri's inequalities on the CR sphere (2007, result): “/p, Cohn and Lu recently made some progress [CoLu1], [CoLu2], deriving the CR analogue of (0.3) with sharp exponential constant in the case of the gradient, p= Q, both on Hn or the CR S2n+1 (see also [BMT] for similar results on Carnot groups). In regards to the “correct” CR analogue of Beckner-Onof”
Affine Moser–Trudinger and Morrey–Sobolev inequalities (2009, unknown): “, [3, 4, 5, 6, 7, 11, 10, 15, 16, 19, 20, 23, 24, 26, 30, 47].”
A new approach to sharp Moser–Trudinger and Adams type inequalities: A rearrangement-free argument (2013, methodology): “We note the Moser–Trudinger inequality on domains of finite measure in the Carnot group was given in [6] which extends the results on the Heisenberg group and groups of Heisenberg type in [14,16].”
Sharp subcritical Moser-Trudinger inequalities on Heisenberg groups and subelliptic PDEs (2014, unknown): “We note theMoser–Trudinger inequality on domains of finitemeasure in the Carnot group was given in [27] which extends the results on the Heisenberg group and groups of Heisenberg type in [11,28].”
Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications ✩ (2012, background): “3 was extended to the groups of Heisenberg type in [20] and to general stratified groups in [8].”
Sharp constants for Moser‐Trudinger inequalities on spheres in complex space ℂn (2004, methodology): “The ideas and methods developed in [17] have also been used to generalize to the Heisenberg-type group in [18] and more general groups in [4].”
Polar coordinates in Carnot groups (2002, methodology): “Corollary 4.5 follows immediately by combining Theorem 2.15(b) with Theorem 4.1 of [ 4 ].”