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Weighted norm inequalities for the conjugate function on $a$-adic solenoids

Weighted norm inequalities for the conjugate function on $a$-adic solenoids

In this paper we generalize a theorem of Hunt, Muckenhoupt, and Wheeden on weighted norm inequalities for the conjugate function.Our generalization to the cases of a-adic solenoids is formulated in terms of the ergodic Ap -condition.