Advances in Mathematics 201 (2006) 209 – 262 www.elsevier.com/locate/aim Extrapolation methods and Rubio de Francia’s extrapolation theorem  Joaquim Martín a , 1 , Mario Milman b, ∗ a Department of Mathematics, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona) Spain b Department of Mathematics, Florida Atlantic University, Boca Raton, FL 33431, USA Received 5 April 2004; received in revised form 5 January 2005; accepted 23 February 2005 Communicated by L. Caffarelli Available online 3 May 2005 To the memory of Jose Luis Rubio de Francia Abstract We develop a general framework to study extrapolation of inequalities. © 2005 Elsevier Inc. All rights reserved. MSC: primary 47B38; 46M35; secondary 42B25; 42B20 Keywords: Weights; Extrapolation; Singular integrals; Factorization Contents 1. Introduction ............................................................. 210 2. Intersections, sums and unions of Banach spaces .......................... 211 3. Examples ............................................................... 219 4. The Jawerth–Milman theory .............................................. 227 5. Operators  and ∑ -factorizable: basic concepts ........................... 232  Most of this research was done while (J. Martín) was visiting Florida Atlantic University (1999–2000). This paper is in final form and no version of it will be submitted for publication elsewhere. ∗ Corresponding author. Fax: +1 561 330 0583. E-mail addresses: jmartin@mat.uab.es (J. Martín), extrapol@bellsouth.net (M. Milman) URL: http://www.math.fau.edu/milman (M. Milman). 1 Supported by “programa Ramón y Cajal (MCYT)”, and supported in part by DGICYT BMF2001–3395 and by CURE 2001SGR 00069. 0001-8708/$ - see front matter © 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.aim.2005.02.006 brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by Elsevier - Publisher Connector