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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, amelas@math.uoa.gr
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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

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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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