Weights, Extrapolation and the Theory of Rubio de Francia

By D. Cruz-Uribe, J. M. Martell, C. P'erez. 2011

512 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ad5bd0117cebffa80d1337859efb7a495cbe5791

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Control and Systems Engineering

In Statistics and Probability

Citations in the corpus

Sharp weighted estimates for classical operators (2010, methodology): “ that A(t) = tp log(e + t)p−1+δ, δ > 0 (here A¯ ∈ B p′), and for Riesz transforms (indeed, for any Caldero´n-Zygmund singular integral) given the additional hypothesis that p > n. Examples (see [7, 8]) show that in this particular case these results are sharp, since they are false in general i”
Extrapolation and weighted norm inequalities in the variable Lebesgue spaces (2014, methodology): “A more general result is possible; see [19, Remark 3.39].”
Extrapolation for multilinear Muckenhoupt classes and applications (2018, background): “For complete discussion of this approach to extrapolation in the linear setting, see [13].”
Maximal Regularity for Non-autonomous Equations with Measurable Dependence on Time (2014, background): “The theory of Rubio de Francia (see [18] and references therein) enables one to extrapolate from weighted L-estimates for a single p ∈ (1, ∞), to any p ∈ (1,∞).”
Vertical versus conical square functions (2010, methodology): “e obtain kSfk2 L2(w) ≤ bn [w]A1 Z Rn Z∞ 0 |f(y,t)|2 dt t w(y)dy= bn [w]A1 kVfk2 L2(w). Next we invoke the Rubio de Francia extrapolation theorem (see [Rub], [Gar] for the original result, and [CMP1], [CMP2] for a statement written in terms of pairs of functions) for the pairs (Sf)2,(Vf)2 : the start”
One and two weight norm inequalities for Riesz potentials (2012, background): “The following result is due to Perez [31] (also see [3]).”
Two weight norm inequalities for fractional integral operators and commutators (2014, background): “However, they do not appear to have ever been published until they appeared in [21].”
The maximal operator on weighted variable Lebesgue spaces (2011, methodology): “Our proof below adapts to the variable exponent case techniques used to prove two-weight norm inequalities for a variety of operators; see [7] for details and further references.”