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A note on the off-diagonal Muckenhoupt-Wheeden conjecture

    https://doi.org/10.1142/9789814699693_0006Cited by:1 (Source: Crossref)
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    Abstract:

    We obtain the off-diagonal Muckenhoupt-Wheeden conjecture for Calderón-Zygmund operators. Namely, given 1 < p < q < ∞ and a pair of weights (u, v), if the Hardy-Littlewood maximal function satisfies the following two weight inequalities:

    then any Calderón-Zygmund operator T and its associated truncated maximal operator T⋆ are bounded from Lp(υ) to Lq(u). Additionally, assuming only the second estimate for M then T and T⋆ map continuously Lp(υ) into Lq,∞(u). We also consider the case of generalized Haar shift operators and show that their off-diagonal two weight estimates are governed by the corresponding estimates for the dyadic Hardy-Littlewood maximal function.