Scopus: 69 cites, Web of Science: 69 cites,
Lp bounds for Riesz transforms and square roots associated to second order elliptic operators
Hofmann, Steve
Martell, José María

Data: 2003
Resum: 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.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: Article ; recerca ; article ; publishedVersion
Matèria: Riesz transforms ; Square roots of divergence form elliptic operators
Publicat a: Publicacions matematiques, V. 47 N. 2 (2003) , p. 497-515, ISSN 0214-1493

Adreça original:
DOI: 10.5565/PUBLMAT_47203_12

19 p, 196.1 KB

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