Sharp two-weight inequalities for singular integrals, with applications to the Hilbert transform and the Sarason conjecture

By D. Cruz-Uribe, J. M. Martell, C. P'erez. 2007

76 citations recorded by the source corpus.

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In Applied Mathematics

Citations in the corpus

A Fractional Muckenhoupt–Wheeden Theorem and its Consequences (2013, background): “Earlier, related estimates for singular integrals were implicit in [2] and the corresponding version of Theorem 3.”
Weighted inequalities for multilinear fractional integral operators (2009, background): “See Cruz-Uribe, Martell, and P´ erez, [ 4 ], for further references and historical remarks.”
Sharp weighted estimates for approximating dyadic operators (2010, methodology): “By way of comparison, in [4] a key technical difficulty resulted from having to use Kolmogorov’s inequality rather than the weak (1, 1) inequality for a singular integral.”
On an estimate of Calderón-Zygmund operators by dyadic positive operators (2012, methodology): “,Q < ∞, then kTfkLp(u) ≤ ckfkLp(v). For a complete history of this conjecture and partial results we refer to a recent book [3]. Under certain restrictions on A and B, the conjecture was proved in [2]. By means of the “local mean oscillation decomposition” the conjecture was proved for any T in t”
Two weight norm inequalities for fractional integral operators and commutators (2014, result): “This problem was solved recently by Lerner [58]; for prior results see [19, 20, 30].”
A characterization of two weight norm inequalities for maximal singular integrals with one doubling measure (2008, background): “, or the Riesz Transforms. This question occurs in dierent instances, such as the Sarason Conjecture concerning the composition of Hankel operators, or the semi-commutator of Toeplitz operators (see [3], [25]), Mathematical Physics [13], as well as perturbation theory of some self-adjoint operators.”
A pointwise estimate for the local sharp maximal function with applications to singular integrals (2010, methodology): “3) has been applied to several problems concerning weighted inequalities for singular integrals: sharp two-weight norm inequalities for T (see [6]) and sharp L(w) estimates in terms of the A1 characteristic of w (see [18]).”