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The Journal of Geometric Analysis

, Volume 29, Issue 2, pp 1109–1115 | Cite as

Dimension-Free Properties of Strong Muckenhoupt and Reverse Hölder Weights for Radon Measures

  • O. Beznosova
  • A. ReznikovEmail author
Article
  • 59 Downloads

Abstract

In this paper, we prove self-improvement properties of strong Muckenhoupt and Reverse Hölder weights with respect to a general Radon measure on \(\mathbb {R}^n\). We derive our result via a Bellman function argument. An important feature of our proof is that it uses only the Bellman function for the one-dimensional problem for Lebesgue measure; with this function in hand, we derive dimension-free results for general measures and dimensions.

Keywords

Bellman function Dimension-free estimates Muckenhoupt weights Reverse Hölder weights 

Mathematics Subject Classification

Primary 42B35 Secondary 43A85 

Notes

Acknowledgements

We are very grateful to Vasiliy Vasyunin for helpful discussions and suggestions on the presentation of this paper.

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Copyright information

© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of AlabamaTuscaloosaUSA
  2. 2.Department of MathematicsFlorida State UniversityTallahasseeUSA

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