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00925njm 22002777a 4500 dc Duoandikoetxea, Javier author Martín Reyes, Francisco J. author Ombrosi, Sheldy Javier author 2015 We discuss several characterizations of the A [infinite] class of weights in the setting of general bases. Although they are equivalent for the usual Muckenhoupt weights, we show that they can give rise to different classes of weights for other bases. We also obtain new characterizations for the usual A [infinite] weights. Duoandikoetxea J, Martín-Reyes FJ, Ombrosi S (2016) On the $$A_{\infty }$$ A ∞ conditions for general bases. Math Z 282(3–4):955–972. https://doi.org/10.1007/s00209-015-1572-y 0025-5874 10.1007/s00209-015-1572-y https://hdl.handle.net/20.500.14352/98568 1432-1823 https://doi.org/10.1007/s00209-015-1572-y On the A [infinite] conditions for general bases