Some new scales of weight characterizations of the class \(B_p\) (Q1046910)

We present an equivalence theorem which includes all known characterizations of the class \(B_p,\) i.e., the weight class of \textit{M. A. Arino} and \textit{B. Muckenhoupt} [Trans. Am. Math. Soc. 320, No.~2, 727--735 (1990; Zbl 0716.42016)], and also some new equivalent characterizations. We also give equivalent characterizations for the classes \(B_p^*\), \(B_{\infty}^*\) and \(RB_p\), and prove and apply a ``gluing lemma'' of independent interest.