Geodesic
On Weighted Norm Inequalities for Fractional and Singular Integrals
Canadian journal of mathematics, Tome 23 (1971) no. 5, pp. 907-928

Voir la notice de l'article provenant de la source Cambridge University Press

In a recent paper [12] Muckenhoupt and Wheeden have established necessary and sufficient conditions for the validity of norm inequalities of the form ‖ |x|αTƒ ‖q ≦ C‖ |x|α ƒ ‖p , where Tƒ denotes a Calderón and Zygmund singular integral of ƒ or a fractional integral with variable kernel. The purpose of the present paper is to prove, by somewhat different methods, similar inequalities for more general weight functions.In what follows, for p ≧ 1, p′ is the exponent conjugate to p, given by l/p + l/p′ = 1. Ω will always denote a locally integrable function on R n which is homogeneous of degree 0, Ω∼ will denote a measurable function on R n × R n such that for each x ∈ R n , Ω∼(x, .) is locally integrable and homogeneous of degree 0. 
Walsh, T. On Weighted Norm Inequalities for Fractional and Singular Integrals. Canadian journal of mathematics, Tome 23 (1971) no. 5, pp. 907-928. doi: 10.4153/CJM-1971-100-1
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