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A SHARP $L^{\lowercase{p}}$ INEQUALITY FOR DYADIC $A_{1}$ WEIGHTS IN $\mathbb{R}^{\lowercase{n}}$

Published online by Cambridge University Press:  12 December 2005

ANTONIOS D. MELAS
ANTONIOS D. MELAS
Affiliation:
Department of Mathematics, University of Athens, Panepistimiopolis 15784, Athens, Greece, [email protected]
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Abstract

The exact best possible range of p is determined such that any dyadic $A_{1}$ weight w on $\mathbb{R}^{n}$ satisfies a reverse Hölder inequality for p, which depends on the dimension n and the corresponding $A_{1}$ constant of w. The proof is based on an effective linearization of the dyadic maximal operator applied to dyadic step functions.

Keywords

42B25
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 6 , December 2005 , pp. 919 - 926
Copyright
© The London Mathematical Society 2005

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