Two-weight norm inequalities for fractional integral operators with $A_{\lambda,\infty}$ weights

Abstract

In this paper, we introduce a new class of weights, the A λ,∞ weights, which contains the classical A ∞ weights. We prove a mixed A p,q-A λ,∞ type estimate for fractional integral operators.

Off-Diagonal Two Weight Bumps for Fractional Sparse Operators

“…This was extended to the general p = q case by Lacey-Spencer in [9]. These operators were also studied in the off-diagonal p ≤ q, α > 0 setting in [16,18]. Our theorem here is "sharp" in the sense that when σ and w are A ∞ , we recover the sharp results of, for example [2,3,7].…”