Rough bilinear singular integrals

Grafakos, Loukas; He, Danqing; Honzík, Petr

doi:10.1016/j.aim.2017.12.013

Cited by 40 publications

(50 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the bilinear setting the role of the crucial L 2 → L 2 estimate is played by an L 2 ×L 2 → L 1 , and obviously Plancherel's identity cannot be used on L 1 . We overcome the lack of orthogonality on L 1 via a wavelet technique introduced by three of the authors in [10] in the study of certain bilinear operators; on this approach…”

Section: Introductionmentioning

confidence: 99%

Bilinear spherical maximal function

Barrionuevo

Grafakos

et al. 2018

Mathematical Research Letters

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Bilinear spherical maximal function

Barrionuevo

Grafakos

et al. 2018

Mathematical Research Letters

Self Cite

View full text Add to dashboard Cite

show abstract

“…but it turns out that the optimal value of the constant α(2, 2) is 1/4. The considerations here are related to the proof of [9, Theorem 1.3], which enhances the combinatorial argument in [6].…”

Section: The Bilinear Problemmentioning

confidence: 99%

“…It is very natural to study multipliers appearing as sums of bumps supported in lattices, as many decompositions in analysis lead to such objects, e.g., wavelets, frames, ϕ transform, etc. Our present study is motivated by the solution of the boundedness problem for rough bilinear singular integrals in the largest possible open set of exponents, obtained in [6]. This solution relies on standard techniques of harmonic analysis but also uses a new treatment of columns of coefficients.…”

mentioning

confidence: 99%

The lattice bump multiplier problem

Buriánková

Grafakos

et al. 2022

Studia Math.

Self Cite

View full text Add to dashboard Cite

We study the lattice bump multiplier problem. Precisely, given a smooth bump supported in a ball centered at the origin, we consider the multiplier formed by adding the translations of this bump centered at N distinct lattice points. We investigate the dependence on N of the L p norm of the linear and bilinear operators associated with this multiplier. We obtain sharp dependence on N in the linear case and in the bilinear case when p > 1.

show abstract

“…A particular case of interest is that of rough bilinear singular integrals introduced by Coifman and Meyer and further studied by [20]. As explained in [27,Section 2.4], either from the weighted estimates obtained in [8] or from the sparse domination from [1] one easily gets an extension of [27,Corollary 2.17] covering the end-point cases.…”

Section: Calderón-zygmund Operators the Bilinear Hilbert Transform mentioning

confidence: 99%

End-point estimates, extrapolation for multilinear Muckenhoupt classes, and applications

Martell

Martikainen

et al. 2020

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

In this paper we present the results announced in the recent work by the first, second, and fourth authors of the current paper concerning Rubio de Francia extrapolation for the so-called multilinear Muckenhoupt classes. Here we consider the situations where some of the exponents of the Lebesgue spaces appearing in the hypotheses and/or in the conclusion can be possibly infinity. The scheme we follow is similar, but, in doing that, we need to develop a one-variable end-point off-diagonal extrapolation result. This complements the corresponding "finite" case obtained by Duoandikoetxea, which was one of the main tools in the aforementioned paper. The second goal of this paper is to present some applications. For example, we obtain the full range of mixed-norm estimates for tensor products of bilinear Calderón-Zygmund operators with a proof based on extrapolation and on some estimates with weights in some mixed-norm class. The same occurs with the multilinear Calderón-Zygmund operators, the bilinear Hilbert transform, and the corresponding commutators with BMO functions. Extrapolation along with the already established weighted norm inequalities easily give scalar and vector-valued inequalities with multilinear weights and these include the end-point cases.

show abstract

Rough bilinear singular integrals

Cited by 40 publications

References 23 publications

Bilinear spherical maximal function

Bilinear spherical maximal function

The lattice bump multiplier problem

End-point estimates, extrapolation for multilinear Muckenhoupt classes, and applications

Contact Info

Product

Resources

About