Ideal weights: Asymptotically optimal versions of doubling, absolute continuity, and bounded mean oscillation

  • Michael Brian Korey
Article

Abstract

Sharp inequalities between weight bounds (from the doubling, Ap, and reverse Hölder conditions) and the BMO norm are obtained when the former are near their optimal values. In particular, the BMO norm of the logarithm of a weight is controlled by the square root of the logarithm of its A bound. These estimates lead to a systematic development of asymptotically sharp higher integrability results for reverse Hölder weights and extend Coifman and Fefferman's formulation of the A condition as an equivalence relation on doubling measures to the setting in which all bounds become optimal over small scales.

Math Subject Classifications

Primary 42B25, 26D15 secondary 26B35 

Keywords and Phrases

Doubling measure bounded mean oscillation A condition reverse Hölder inequality MuckenhouptAp condition arithmetic-geometric inequality 

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Copyright information

© Birkhäuser Boston 1998

Authors and Affiliations

  • Michael Brian Korey
    • 1
  1. 1.Institut für MathematikUniversität PotsdamPotsdamGermany

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