On the best constant for the Friedrichs-Knapp-Stein inequality in free nilpotent Lie groups of step two and applications to subelliptic PDE

Domokos, András; Fanciullo, Maria Stella

doi:10.1007/bf02930723

Cited by 4 publications

(5 citation statements)

References 11 publications

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“…For the proof we need the difference quotient method from [2] developed for non-nilpotent cases and the Cordes technique from [7,8,16]. The proof is similar in every aspect to what is found in the above cited papers, so we invite the interested reader to check the details.…”

Section: Theorem 43mentioning

confidence: 91%

“…Our paper proposes to use the tools of the noncommutative harmonic analysis and the representation theory of semisimple Lie groups to estimate C in non-nilpotent subelliptic structures and by this, extend the results from [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

“…The existence of C has been proved for general subelliptic structures (see [3][4][5]), but its estimation was done just in certain nilpotent cases, nice as the Grušin plane, Heisenberg group and free nilpotent Lie groups of step two on an even number of generators [6][7][8] or on strictly pseudo-convex pseudo-Hermitian manifolds [9]. Our paper proposes to use the tools of the noncommutative harmonic analysis and the representation theory of semisimple Lie groups to estimate C in non-nilpotent subelliptic structures and by this, extend the results from [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Subelliptic estimates on compact semisimple Lie groups

Domokos

Esquerra

Jaffa

et al. 2011

Nonlinear Analysis: Theory, Methods & Applications

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Section: Theorem 43mentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Subelliptic estimates on compact semisimple Lie groups

Domokos

Esquerra

Jaffa

et al. 2011

Nonlinear Analysis: Theory, Methods & Applications

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“…For the free nilpotent Lie group of step two on 2n generators denoted by F 2n,2 , the related harmonic analysis and Radon transform were studied by Strichartz [24]. Inspired by this work, the best constant for the Friedrichs-Knapp-Stein inequality on F 2n,2 was discussed by Domokos and Franciullo [3]. For more general research on free nilpotent Lie groups of step two, we refer the reader to [1,5].…”

Section: The Case Of Radon Transform On the Euclidean Spacementioning

confidence: 99%

Inversion of the Radon Transform on the Free Nilpotent Lie Group of Step Two

Xiao

2014

Can. j. math.

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Abstract. Let F 2n,2 be the free nilpotent Lie group of step two on 2n generators, and let P denote the affine automorphism group of F 2n,2 . In this article the theory of continuous wavelet transform on F 2n,2 associated with P is developed, and then a type of radial wavelets is constructed. Secondly, the Radon transform on F 2n,2 is studied and two equivalent characterizations of the range for Radon transform are given. Several kinds of inversion Radon transform formulae are established. One is obtained from the Euclidean Fourier transform, the others are from group Fourier transform. By using wavelet transform we deduce an inversion formula of the Radon transform, which does not require the smoothness of functions if the wavelet satisfies the differentiability property. Specially, if n = 1, F 2,2 is the 3-dimensional Heisenberg group H 1 , the inversion formula of the Radon transform is valid which is associated with the sub-Laplacian on F 2,2 . This result cannot be extended to the case n ≥ 2.

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“…In the case of (1) on a CR manifold a result has been recently obtained by Domokos-Manfredi [6] in the Heisenberg group. The proof in [6] makes uses of the harmonic analysis techniques in the Heisenberg group developed by Strichartz [16] that will not apply to studying such inequalities for the Hessian on a general CR manifold, although other nilpotent groups of step 2 can be treated similarly [5]. Instead we shall proceed by integration by parts and use of the Bochner technique.…”

Section: Introductionmentioning

confidence: 99%