Lp bounds for Riesz transforms and square roots associated to second order elliptic operators

• Autores: Steve Hofmann, José María Martell Berrocal
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 47, Nº 2, 2003, págs. 497-515
• Idioma: inglés
• DOI: 10.5565/publmat_47203_12
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• Resumen

  • We consider the Riesz transforms ∇L−1/2, where L≡− divA(x)∇, and A is an accretive, n × n matrix with bounded measurable complex entries, defined on Rn. We establish boundedness of these operators on Lp(Rn), for the range pn < p ≤ 2, where pn = 2n/(n + 2), n ≥ 2, and we obtain a weak-type estimate at the endpoint pn. The case p = 2 was already known: it is equivalent to the solution of the square root problem of T. Kato.