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

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.