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Pré-Publication, Document De Travail Année : 2014

Sharp $L^p$ estimates for second order Riesz transforms on multiply–connected Lie groups

Résumé

We study a class of combinations of second order Riesz transforms on Lie groups $G = G_x \times G_y$ that are multiply connected, composed of a discrete abelian component $G_x$ and a compact connected component $G_y$ . We prove sharp $L^p$ estimates for these operators, therefore generalizing previous results [13][4]. The proof uses stochastic integrals with jump components adapted to functions defined on the semi-discrete set $G = G_x \times G_y$ . The analysis shows that Itô integrals for the discrete component must be written in an augmented discrete tangent plane of dimension twice larger than expected, and in a suitably chosen discrete coordinate system. Those artifacts are related to the difficulties that arise due to the discrete component, where derivatives of functions are no longer local.
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Dates et versions

hal-01087434 , version 1 (26-11-2014)

Identifiants

  • HAL Id : hal-01087434 , version 1

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N Arcozzi, Komla Domelevo, Stefanie Petermichl. Sharp $L^p$ estimates for second order Riesz transforms on multiply–connected Lie groups. 2014. ⟨hal-01087434⟩
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