Distributions that are convolvable with generalized Poisson kernel of solvable extensions of homogeneous Lie groups
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Autores: E. Damek, Jacek Dziubanski
, Jaming Philippe, Salvador Pérez-Esteva
- Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 105, Nº 1, 2009, págs. 31-65
- Idioma: inglés
- DOI: 10.7146/math.scand.a-15105
- Enlaces
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Resumen
In this paper, we characterize the class of distributions on a homogeneous Lie group N that can be extended via Poisson integration to a solvable one-dimensional extension S of N. To do so, we introduce the S′-convolution on N and show that the set of distributions that are S′-convolvable with Poisson kernels is precisely the set of suitably weighted derivatives of L1-functions. Moreover, we show that the S′-convolution of such a distribution with the Poisson kernel is harmonic and has the expected boundary behavior. Finally, we show that such distributions satisfy some global weak-L1 estimates.
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