Extrapolation and sharp norm estimates for classical operators on weighted Lebesgue spaces

Dragičević, Oliver; Grafakos, Loukas; Pereyra, María; Petermichl, Stefanie

doi:10.5565/publmat_49105_03

Cited by 101 publications

(110 citation statements)

References 20 publications

Supporting

Mentioning

107

Contrasting

Order By: Relevance

“…By the sharp form of Rubio de Francia's extrapolation theorem due to Dragičević, Grafakos, Pereyra and Petermichl [6], this implies the corresponding weighted L p bound,…”

Section: Introductionmentioning

confidence: 99%

The sharp weighted bound for general Calderón--Zygmund operators

2012

View full text Add to dashboard Cite

For a general Calderón-Zygmund operator T on R N , it is shown thatfor all Muckenhoupt weights w ∈ A2. This optimal estimate was known as the A2 conjecture. A recent result of Pérez-Treil-Volberg reduced the problem to a testing condition on indicator functions, which is verified in this paper. The proof consists of the following elements: (i) a variant of the NazarovTreil-Volberg method of random dyadic systems with just one random system and completely without "bad" parts; (ii) a resulting representation of a general Calderón-Zygmund operator as an average of "dyadic shifts;" and (iii) improvements of the Lacey-Petermichl-Reguera estimates for these dyadic shifts, which allow summing up the series in the obtained representation.

show abstract

“…By the sharp form of Rubio de Francia's extrapolation theorem due to Dragičević, Grafakos, Pereyra and Petermichl [6], this implies the corresponding weighted L p bound,…”

Section: Introductionmentioning

confidence: 99%

The sharp weighted bound for general Calderón--Zygmund operators

2012

View full text Add to dashboard Cite

show abstract

“…Consult also the works of Gundy and Wheeden [9], Dragičević et al [8] and Lerner [12,13] for related results. See also the book by Wilson [25] for an overview of weighted square function inequalities.…”

Section: Introductionmentioning

confidence: 99%

Weighted square function inequalities

Oşekowski¹

2018

Publicacions Matemàtiques

View full text Add to dashboard Cite

show abstract

“…For 1 ≤ p < 2 the operator norm is of the order [w] 1/(p−1) Ap and this is optimal [DGPPet,Sec 4.1]. However for p > 2 the linear results obtained by extrapolation in [DGPPet] are not optimal.…”

Section: Discussionmentioning

confidence: 99%

Haar multipliers meet Bellman functions

Pereyra¹

2009

Rev. Mat. Iberoam.

View full text Add to dashboard Cite

Using Bellman function techniques, we obtain the optimal dependence of the operator norms in L 2 (R) of the Haar multipliers T t w on the correspondingcharacteristic of the weight w, for t = 1, ±1/2. These results can be viewed as particular cases of estimates on homogeneous spaces L 2 (vdσ), for σ a doubling positive measure and v ∈ A d 2 (dσ), of the weighted dyadic square function S d σ . We show that the operator norms of such square functions in L 2 (vdσ) are bounded by a linear function of the A d 2 (dσ) characteristic of the weight v, where the constant depends only on the doubling constant of the measure σ. We also show an inverse estimate for S d σ . Both results are known when dσ = dx. We deduce both estimates from an estimate for the Haar multiplier (2 . The estimate for the Haar multiplier adapted to the σ measure, (T σ v ) 1/2 , is proved using Bellman functions. These estimates are sharp in the sense that the rates cannot be improved and be expected to hold for all σ, since the particular case dσ = dx, v = w, correspond to the estimates for the Haar multipliers T 1/2 w proven to be sharp.

show abstract

Extrapolation and sharp norm estimates for classical operators on weighted Lebesgue spaces

Cited by 101 publications

References 20 publications

The sharp weighted bound for general Calderón--Zygmund operators

The sharp weighted bound for general Calderón--Zygmund operators

Weighted square function inequalities

Haar multipliers meet Bellman functions

Contact Info

Product

Resources

About