  Muckenhoupt and Reverse H\"{o}lder classes of weights play an important role
in harmonic analysis, PDE's and quasiconformal mappings. In 1974 Coifman and
Fefferman showed that a weight belongs to a Muckenhoupt class $A_p$ for some
$1<p<\infty$ if and only if it belongs to a Reverse H\"{o}lder class $RH_q$ for
some $1<q<\infty$. In 2009 Vasyunin found the exact dependence between $p$, $q$
and the corresponding characteristic of the weight using the Bellman function
method. The result of Coifman and Fefferman works for the dyadic classes of
weights under an additional assumption that the weights are dyadically
doubling. We extend the Vasyunin's result to the dyadic Reverse H\"{o}lder and
Muckenhoupt classes and obtain the dependence between $p$, $q$, the doubling
constant and the corresponding characteristic of the weight. More precisely,
given a dyadically doubling weight in $RH_p^d$ on a given dyadic interval $I$,
we find an upper estimate on the average of the function $w^{q}$ over the
interval $I$. From the bound on this average we can conclude, for example, that
$w$ belongs to the corresponding $A_{s_1}^d$ class or that $w^p$ is in
$A_{s_2}^d$ for some values of $s_i$. We obtain our results using the method of
Bellman functions.
