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We give a classification between weighted norm inequalities of strong fractional integral operators and their corresponding multi-parameter Muckenhoupt characteristics, by considering the weights to be power functions. As a result, we extend the classical Stein–Weiss theorem on product spaces.
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Zipeng Wang, Stein–Weiss inequality on product spaces. Rev. Mat. Iberoam. 37 (2021), no. 5, pp. 1641–1667DOI 10.4171/RMI/1244