Lp-estimates for Riesz transforms on forms in the Poincaré space
Bruna, Joaquim (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Fecha:	2005
Resumen:	Using hyperbolic form convolution with doubly isometry-invariant kernels, the explicit expression of the inverse of the de Rham laplacian ∆ acting on m-forms in the Poincaré space Hn is found. Also, by means of some estimates for hyperbolic singular integrals, Lp-estimates for the Riesz transforms ∆i∆Ñ−1, i ≤ 2, in a range of p depending on m, n are obtained. Finally, using these, it is shown that ∆ defines topological isomorphisms in a scale of Sobolev spaces Hs mp („Hn) in case m≠ („n ± 1) /2, n/2.
Derechos:	Tots els drets reservats.
Lengua:	Anglès
Documento:	Article ; Versió publicada
Materia:	Hodge-de Rham laplacian ; Sobolev spaces ; Riesz transforms ; Hyperbolic form convolution
Publicado en:	Indiana University mathematics journal, Vol. 54, No. 1 (2005) , p. 153-187, ISSN 0022-2518

DOI: 10.1512/iumj.2005.54.2501

34 p, 311.9 KB

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