Sparse Domination and Weighted Estimates for Rough Bilinear Singular Integrals

Grafakos, Loukas; Wang, Zhidan; Xue, Qingying

doi:10.1007/s00041-022-09973-z

Cited by 3 publications

(1 citation statement)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The sparse domination and weighted inequalities of linear and multilinear rough singular integrals are natural questions that arise upon establishing their

L^p

boundedness in (). These problems in the linear and bilinear settings actually have been studied by [1, 3, 4, 10, 24, 27]. Our goal in this work is not to establish a comprehensive study of these operators, but to provide boundedness tools that will play a crucial role in their further investigation, including that of their sparse domination properties and their weighted estimates.…”

Section: Introductionmentioning

confidence: 99%

Multilinear rough singular integral operators

Grafakos,

He,

Honzík

et al. 2024

Journal of London Math Soc

Self Cite

View full text Add to dashboard Cite

show abstract

“…The sparse domination and weighted inequalities of linear and multilinear rough singular integrals are natural questions that arise upon establishing their

L^p

Section: Introductionmentioning

confidence: 99%

Multilinear rough singular integral operators

Grafakos,

He,

Honzík

et al. 2024

Journal of London Math Soc

Self Cite

View full text Add to dashboard Cite

show abstract

Limited Range Extrapolation with Quantitative Bounds and Applications

Cao,

Liu,

et al. 2024

J Fourier Anal Appl

View full text Add to dashboard Cite

In recent years, sharp or quantitative weighted inequalities have attracted considerable attention on account of the $$A_2$$ A 2 conjecture solved by Hytönen. Advances have greatly improved conceptual understanding of classical objects such as Calderón–Zygmund operators. However, plenty of operators do not fit into the class of Calderón–Zygmund operators and fail to be bounded on all $$L^p(w)$$ L p ( w ) spaces for $$p \in (1, \infty )$$ p ∈ ( 1 , ∞ ) and $$w \in A_p$$ w ∈ A p . In this paper we develop Rubio de Francia extrapolation with quantitative bounds to investigate quantitative weighted inequalities for operators beyond the (multilinear) Calderón–Zygmund theory. We mainly establish a quantitative multilinear limited range extrapolation in terms of exponents $$p_i \in (\mathfrak {p}_i^-, \mathfrak {p}_i^+)$$ p i ∈ ( p i - , p i + ) and weights $$w_i^{p_i} \in A_{p_i/\mathfrak {p}_i^-} \cap RH_{(\mathfrak {p}_i^+/p_i)'}$$ w i p i ∈ A p i / p i - ∩ R H ( p i + / p i ) ′ , $$i=1, \ldots , m$$ i = 1 , … , m , which refines a result of Cruz-Uribe and Martell. We also present an extrapolation from multilinear operators to the corresponding commutators. Additionally, our result is quantitative and allows us to extend special quantitative estimates in the Banach space setting to the quasi-Banach space setting. Our proof is based on an off-diagonal extrapolation result with quantitative bounds. Finally, we present various applications to illustrate the utility of extrapolation by concentrating on quantitative weighted estimates for some typical multilinear operators such as bilinear Bochner–Riesz means, bilinear rough singular integrals, and multilinear Fourier multipliers. In the linear case, based on the Littlewood–Paley theory, we include weighted jump and variational inequalities for rough singular integrals.

show abstract

Bilinear sparse domination for oscillatory integral operators

Mattsson

2024

Anal.Math.Phys.

View full text Add to dashboard Cite

In this paper, we prove bilinear sparse domination bounds for a wide class of Fourier integral operators of general rank, as well as oscillatory integral operators associated to Hörmander symbol classes $$S^m_{\rho ,\delta }$$ S ρ , δ m for all $$0\le \rho \le 1$$ 0 ≤ ρ ≤ 1 and $$0\le \delta < 1$$ 0 ≤ δ < 1 , a notable example is the Schrödinger operator. As a consequence, one obtains weak (1, 1) estimates, vector-valued estimates, and a wide range of weighted norm inequalities for these classes of operators.

show abstract

Sparse Domination and Weighted Estimates for Rough Bilinear Singular Integrals

Cited by 3 publications

References 34 publications

Multilinear rough singular integral operators

Multilinear rough singular integral operators

Limited Range Extrapolation with Quantitative Bounds and Applications

Bilinear sparse domination for oscillatory integral operators

Contact Info

Product

Resources

About