Multilinear square functions and multiple weights

@article{Grafakos2019MultilinearSF,
  title={Multilinear square functions and multiple weights},
  author={Loukas Grafakos and Parasar Mohanty and Saurabh Shrivastava},
  journal={MATHEMATICA SCANDINAVICA},
  year={2019}
}
In this paper we prove weighted estimates for a class of smooth multilinear square functions with respect to multilinear $A_{\vec P}$ weights. In particular, we establish weighted estimates for the smooth multilinear square functions associated with disjoint cubes of equivalent side-lengths. As a consequence, for this particular class of multilinear square functions, we provide an affirmative answer to a question raised by Benea and Bernicot (Forum Math. Sigma 4, 2016, e26) about unweighted… 

References

SHOWING 1-10 OF 19 REFERENCES
Domination of multilinear singular integrals by positive sparse forms
TLDR
This work establishes a uniform domination of the family of trilinear multiplier forms with singularity over a one-dimensional subspace by positive sparse forms involving $L^p$-averages and obtains-boundedness of the bilinear Hilbert transform when the weights $v_j$ belong to the class A_{\frac{q+1}{2}}\cap RH_2$.
Lp estimates for non smooth bilinear Littlewood-Paley square functions on R
In this work, some non smooth bilinear analogues of linear Littlewood-Paley square functions on the real line are studied. These bilinear operators are closely related to the bilinear Hilbert
A remark on bilinear Littlewood–Paley square functions
The aim of this note is to point out that the results proved in Bernicot and Shrivastava (Indiana Univ Math J 60(1):233–268, 2011) and Ratnakumar and Shrivastava (Proc Am Math Soc 140(12):4285–4293,
Boundedness of smooth bilinear square functions and applications to some bilinear pseudo-differential operators
This paper is devoted to the proof of boundedness of bilinear smooth square functions. Moreover, we deduce boundedness of some bilinear pseudo-differential operators associated with symbols belonging
Multilinear Calderón–Zygmund Theory
Abstract A systematic treatment of multilinear Calderon–Zygmund operators is presented. The theory developed includes strong type and endpoint weak type estimates, interpolation, a multilinear T 1
A note on the bilinear Littlewood-Paley square function
. In this paper, we give an elementary proof of boundedness of the smooth bilinear Littlewood-Paley square function.
Lp estimates for non-smooth bilinear Littlewood–Paley square functions on $${\mathbb{R}}$$
AbstractIn this work, we study some non-smooth bilinear analogues of linear Littlewood–Paley square functions on the real line. We prove boundedness-properties in Lebesgue spaces for them. Let us
Some remarks on bilinear Littlewood–Paley theory☆
The Sharp Weighted Bound for Multilinear Maximal Functions and Calderón–Zygmund Operators
TLDR
The sharp bound for the multilinear maximal function for all such p_1, p_m, p1,…,pm is proved and that of m-linear Calderón–Zymund operators when p≥1 is proved.
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