  In the dyadic case the union of the Reverse H\"{o}lder classes, $RH_p^d$ is
strictly larger than the union of the Muckenhoupt classes $ A_p^d$. We
introduce the $RH_1^d$ condition as a limiting case of the $RH_p^d$
inequalities as $p$ tends to 1 and show the sharp bound on $RH_1^d$ constant of
the weight $w$ in terms of its $A_\infty^d$ constant.
  We also take a look at the summation conditions of the Buckley type for the
dyadic Reverse H\"{o}lder and Muckenhoupt weights and deduce them from an
intrinsic lemma which gives a summation representation of the bumped average of
a weight. Our lemmata also allow us to obtain summation conditions for
continuous Reverse H\"{o}lder and Muckenhoupt classes of weights and both
continuous and dyadic weak Reverse H\"{o}lder classes. In particular, it shows
that a weight belongs to the class $RH_1$ if and only if it satisfies Buckley's
inequality. We also show that the constant in each summation inequality of
Buckley's type is comparable to the corresponding Muckenhoupt or Reverse
H\"{o}lder constant.
