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Concrete Operators

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On Entropy Bumps for Calderón-Zygmund Operators

Michael T. Lacey
  • Corresponding author
  • School of Mathematics, Georgia Institute of Technology, Atlanta GA 30332, USA,
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Scott Spencer
  • Corresponding author
  • School of Mathematics, Georgia Institute of Technology, Atlanta GA 30332, USA,
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-06-18 | DOI: https://doi.org/10.1515/conop-2015-0003

Abstract

We study twoweight inequalities in the recent innovative language of ‘entropy’ due to Treil-Volberg. The inequalities are extended to Lp, for 1 < p ≠ 2 < ∞, with new short proofs. A result proved is as follows. Let ɛ be a monotonic increasing function on (1,∞) which satisfy Let σ and w be two weights on ℝd. If this supremum is finite, for a choice of 1 < p < ∞,

then any Calderón-Zygmund operator T satisfies the bound ||Tof||Lp(w) ≲ ||f|| Lp(o).

Keywords : weighted inequality; Ap; bumps; entropy

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About the article

Received: 2015-03-11

Accepted: 2015-05-19

Published Online: 2015-06-18


Citation Information: Concrete Operators, Volume 2, Issue 1, ISSN (Online) 2299-3282, DOI: https://doi.org/10.1515/conop-2015-0003.

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© 2015 Michael T. Lacey et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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