Tohoku Mathematical Journal
2003
March
SECOND SERIES VOL. 55, NO. 1

Tohoku Math. J.
55 (2003), 109-129

Title SHARP WEIGHTED ESTIMATES FOR VECTOR-VALUED SINGULAR INTEGRAL OPERATORS AND COMMUTATORS

Author Carlos Pérez and Rodrigo Trujillo-González

(Received February 26, 2001, revised November 27, 2001)
Abstract. We prove sharp weighted norm inequalities for vector-valued singular integral operators and commutators. We first consider the strong $(p,p)$ case with $p>1$ and then the weak-type (1,1) estimate. Our results do not assume any condition on the weight function and involve iterations of the classical Hardy-Littlewood maximal function.

2000 Mathematics Subject Classification. Primary 42B20; Secondary 42B25.
Key words and phrases. Singular integral operators, maximal functions, weights.

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