ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 42, 26, 28 Korey, Michael Brian, Universität Potsdam, Germany Optimal Factorization of Muckenhoupt Weights Peter Jones’ theorem on the factorization of A_{p} weights [cf. Annals of Math. 111 (1980), 511–530] is sharpened for weights with bounds near 1, allowing the factorization to be performed continuously near the limiting, unweighted case. When 1 < p < ∞ and w is an A_{p} weight with bound A_{p}(w) = 1 + ε, it is shown that there exist A_{1} weights u, v such that both the formula w = uv^{1−p} and the estimates A_{1}(u), A_{1}(v) = 1 + O(\sqrt{ε}) hold. The square root in the last estimates is also proven to be the correct asymptotic power.