Multiple weighted estimates for vector-valued commutators of multilinear square functions

AbstractWe extend the local non-homogeneous Tb theorem of Nazarov, Treil and Volberg to the setting of singular integrals with operator-valued kernel that act on vector-valued functions. Here, ‘vector-valued’ means ‘taking values in a function lattice with the UMD (unconditional martingale differences) property’. A similar extension (but for general UMD spaces rather than UMD lattices) of Nazarov-Treil-Volberg's global non-homogeneous Tb theorem was achieved earlier by the first author, and it has found applications in the work of Mayboroda and Volberg on square-functions and rectifiability. Our local version requires several elaborations of the previous techniques, and raises new questions about the limits of the vector-valued theory.

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Weighted estimates for vector-valued commutators of multilinear operators

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210504000976 ◽

2008 ◽

Vol 138 (04) ◽

pp. 897-921 ◽

Cited By ~ 18

Author(s):

Lin Tang

Keyword(s):

Multilinear Operators ◽

Weighted Estimates ◽

Vector Valued

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Weighted Vector-Valued Inequalities for a Class of Multilinear Singular Integral Operators

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091517000153 ◽

2018 ◽

Vol 61 (2) ◽

pp. 413-436 ◽

Cited By ~ 1

Author(s):

Guoen Hu ◽

Kangwei Li

Keyword(s):

Singular Integral ◽

Integral Operators ◽

Singular Integral Operators ◽

Maximal Operators ◽

Weighted Estimates ◽

Multilinear Singular Integral ◽

Multiple Weights ◽

Vector Valued

AbstractIn this paper, some weighted vector-valued inequalities with multiple weights $A_{\vec P}$ (ℝmn)are established for a class of multilinear singular integral operators. The weighted estimates for the multi(sub)linear maximal operators which control the multilinear singular integral operators are also considered.

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Weighted Estimates for Rough Maximal Functions with Applications to Angular Integrability

Journal of Function Spaces ◽

10.1155/2019/4976351 ◽

2019 ◽

Vol 2019 ◽

pp. 1-10

Author(s):

Feng Liu ◽

Fangfang Xu

Keyword(s):

Function Spaces ◽

Maximal Functions ◽

Rough Kernels ◽

Weighted Estimates ◽

Polynomial Curves ◽

Definition Of ◽

Vector Valued Function ◽

Vector Valued

In this note we establish certain weighted estimates for a class of maximal functions with rough kernels along “polynomial curves” on Rn. As applications, we obtain the bounds of the above operators on the mixed radial-angular spaces, on the vector-valued mixed radial-angular spaces, and on the vector-valued function spaces. Particularly, the above bounds are independent of the coefficients of the polynomials in the definition of the operators.

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