A unified approach to Carleson measures and A_p weights. II

Francisco José Ruiz and José Luis Torrea

Vol. 120 (1985), No. 1, 189–197

DOI: 10.2140/pjm.1985.120.189

Abstract

In this note we find for each p, 1 < p < ∞, a necessary and sufficient condition on the pair (μ,v) (where μ is a measure on R₊ⁿ⁺¹ = Rⁿ × [0,∞), and v a weight on Rⁿ) for the Poisson integral to be a bounded operator from L^p(Rⁿ,v(x)dx) into L^p(R₊ⁿ⁺¹,μ).

Mathematical Subject Classification 2000

Primary: 42B25

Secondary: 46E30

Milestones

Received: 21 November 1983

Revised: 4 April 1984

Published: 1 November 1985