Moser-Trudinger and Beckner-Onofri's inequalities on the CR sphere

By T. Branson, Luigi Fontana, Carlo Morpurgo. 2007

164 citations recorded by the source corpus.

We derive sharp Moser-Trudinger inequalities on the CR sphere. The rst type is in the Adams form, for powers of the sublaplacian and for general spectrally dened operators on the space of CR-pluriharmonic functions. We will then obtain the sharp Beckner-Onofri inequality for CRpluriharmonic functions on the sphere and, as a consequence, a sharp logarithmic Hardy-Littlewood-Sobolev inequality in the form given by Carlen and Loss.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f1eed935bdd4fac504757c915227ae55a0b5afc1

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Equivalent Moser type inequalities in R2 and the zero mass case (2014, background): “Further generalizations and closely related problems can be found in [12, 11, 23, 32, 52].”
A new approach to sharp Moser–Trudinger and Adams type inequalities: A rearrangement-free argument (2013, background): “We also refer the reader to the sharp Moser inequality with mean value zero by Chang and Yang [11], Lu and Yang [43], Leckband [34], sharp Moser–Trudinger trace inequalities and sharp Moser–Trudinger inequalities without boundary conditions by Cianchi [12,13], the sharp Moser–Trudinger type inequali”
Hardy's inequality for fractional powers of the sublaplacian on the Heisenberg group (2015, methodology): “The HLS inequality as stated in [11] reads as Γ ( 1+n+s 2 )2 Γ ( 1+n−s 2 )2ω s n+1 2n+1 (∫”
An extension problem for the CR fractional Laplacian (2013, methodology): “In the particular case of the Heisenberg group Hn, they are simply the intertwining operators on the CR sphere calculated in [8, 51, 9] using classical representation theory tools.”
Adams inequalities on measure spaces (2009, unknown): “ O(s−p′−σ) (76) for suitable σ>0, with Aas in (75), with equality if the sup in (75) is attained in Ω. Moreover, sup y∈Ω |{x∈ Ω : |K(x,y)| >s}| ≤ Cs−p′. (77) Note. A similar lemma was proved in [BFM], Lemma 2.3, for kernels in the CR sphere. Proof of Lemma 9. From now on we will use the notati”
Hardy and uncertainty inequalities on stratified Lie groups (2013, background): “These were apparently first noticed by Hirschman [22]; other important work on the topic includes [4, 29], and, in the context of nilpotent groups, [7].”
Sharp constants in several inequalities on the Heisenberg group (2010, unknown): “, [Her70], [Ono82], [CY87], [BFM07]), that this can be assumed, and we give a proof of this fact in Appendix B.”
Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications ✩ (2012, unknown): “…the sharp Hardy–Littlewood–Sobolev inequality (1.3) is consistent with Branson, Fontana and Morpurgo's natural guess initially made in their work [14] where among other things, important progress has been made on sharp Onfri–Beckner inequalities on CR spheres (see also earlier work of Cohn and…”