Revista Matemática Iberoamericana


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Volume 35, Issue 6, 2019, pp. 1677–1692
DOI: 10.4171/rmi/1097

Published online: 2019-09-10

Characterizations of a limiting class $B_\infty$ of Békollé–Bonami weights

Alexandru Aleman[1], Sandra Pott[2] and María Carmen Reguera[3]

(1) Lund University, Sweden
(2) Lund University, Sweden
(3) Lund University, Sweden, and University of Birmingham, UK

We explore properties of the class of Békollé–Bonami weights $B_\infty$ introduced by the authors in a previous work. Although Békollé–Bonami weights are known to be ill-behaved because they do not satisfy a reverse Hölder property, we prove than when restricting to a class of weights that are "nearly constant on top halves", one recovers some of the classical properties of Muckenhoupt weights. We also provide an application of this result to the study of the spectra of certain integral operators

Keywords: Bekollé weights, reverse Hölder property, integral operator

Aleman Alexandru, Pott Sandra, Reguera María Carmen: Characterizations of a limiting class $B_\infty$ of Békollé–Bonami weights. Rev. Mat. Iberoam. 35 (2019), 1677-1692. doi: 10.4171/rmi/1097