Geodesic
Relation between the~Gurov--Reshetnyak and the~Muckenhoupt function classes
Sbornik. Mathematics, Tome 194 (2003) no. 6, pp. 919-926

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In the one-dimensional case, for a function satisfying the Gurov–Reshetnyak condition, the infimum of the indices of the Muckenhoupt classes containing this function is found. It is also shown that each Muckenhoupt class lies in some Gurov–Reshetnyak class. 
@article{SM_2003_194_6_a6,
     author = {A. A. Korenovskii},
     title = {Relation  between {the~Gurov--Reshetnyak} and {the~Muckenhoupt} function classes},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
     volume = {194},
     number = {6},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_6_a6/}
}
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A. A. Korenovskii. Relation  between the~Gurov--Reshetnyak and the~Muckenhoupt function classes. Sbornik. Mathematics, Tome 194 (2003) no. 6, pp. 919-926. http://geodesic.mathdoc.fr/item/SM_2003_194_6_a6/