A unified approach to Carleson measures and A_p weights

Francisco José Ruiz

Vol. 117 (1985), No. 2, 397–404

DOI: 10.2140/pjm.1985.117.397

Abstract

In the present note, for each p (1 < p < ∞), we find a condition on the pair (μω) (where μ is a measure on R₊ⁿ⁺¹ and ω a weight) for the Poisson integral to be a bounded operator from L^p(Rⁿ;ω(x)dx) into weak-L^p(R₊ⁿ⁺¹,μ).

Our Theorem I includes, on the one hand, the results of Carleson [1] and Fefferman-Stein [2] concerning the boundedness of the Poisson integral and, on the other hand, Muckenhoupt’s results concerning A_p-weights.

Mathematical Subject Classification 2000

Primary: 42B25

Secondary: 47G05

Milestones

Received: 28 June 1983

Revised: 21 September 1983

Published: 1 April 1985