# Weighted Lipschitz estiamtes for commutators of one-sided operators on one-sided Triebel-Lizorkin spaces

@article{Fu2012WeightedLE, title={Weighted Lipschitz estiamtes for commutators of one-sided operators on one-sided Triebel-Lizorkin spaces}, author={Zun Wei Fu and Qingyan Wu and Guanglie Wang}, journal={arXiv: Functional Analysis}, year={2012} }

Using the extrapolation of one-sided weights, we establish the boundedness of commutators generated by weighted Lipschitz functions and one-sided singular integral operators from weighted Lebesgue spaces to weighted one-sided Triebel-Lizorkin spaces. The corresponding results for commutators of one-sided discrete square functions are also obtained.

## One Citation

Lipschitz Estimates for One-Sided Cohen’s Commutators on Weighted One-Sided Triebel-Lizorkin Spaces

- Mathematics
- 2014

We introduce one-sided Cohen’s commutators of singular integral operators and fractional integral operators, respectively. Using the extrapolation of one-sided weights, we establish the boundedness…

## References

SHOWING 1-10 OF 28 REFERENCES

One-sided Triebel-Lizorkin space and its applications

- Mathematics
- 2011

The authors introduced a class of spaces, called one-sided Triebel-Lizorkin spaces. Using extrapolation of one-sided weights, they studied the boundedness of commutators generated by one-sided…

Weights for commutators of the one-sided discrete square function, the Weyl fractional integral and other one-sided operators

- MathematicsProceedings of the Royal Society of Edinburgh: Section A Mathematics
- 2005

The purpose of this paper is to prove strong-type inequalities with one-sided weights for commutators (with symbol b ∈ BMO) of several one-sided operators, such as the one-sided discrete square…

Two weight norm inequalities for communtators of one-sided singular integrals and the one-sided discrete square function

- MathematicsJournal of the Australian Mathematical Society
- 2005

Abstract The purpose of this paper is to prove strong type inequalities with pairs of related weights for commutators of one-sided singular integrals (given by a Calderón-Zygmund kernel with support…

Weighted inequalities for commutators of one-sided singular integrals

- Mathematics
- 2002

We prove weighted inequalities for commutators of one-sided singular integrals (given by a Calderón-Zygmund kernel with support in (−∞, 0)) with BMO functions. We give the one-sided version of the…

WEIGHTED INEQUALITIES FOR COMMUTATORS OF FRACTIONAL AND SINGULAR INTEGRALS

- Mathematics
- 1991

We dedicate this paper to the memory of José Luis Rubio de Francia, who developed the theory of extrapolation and gave beautiful applications of vectorial methods in harmonic analysis . Through this…

On one-sided BMO and Lipschitz functions

- Mathematics
- 1998

Two basic results concerning functions with conditions on the mean
oscillation are extended to the one-sided setting: the estimate of its distance to L °°
and the pointwise one-sided regularity. In…

WEIGHTED LIPSCHITZ ESTIMATES FOR COMMUTATORS OF FRACTIONAL INTEGRALS WITH HOMOGENEOUS KERNELS

- Mathematics
- 2011

In this paper the authors give a sufficient condition such that the commutator generated by the weighted Lipschitz function and the fractional integral operator with homogeneous kernel satisfying…

Weighted norm inequalities for the Riemann-Liouville and Weyl fractional integral operators

- Mathematics
- 1988

Caracterisation des fonctions-poids pour lesquelles l'operateur integral fractionnaire de Riemann-Liouville d'ordre α>0 est borne

Two weight inequalities for fractional one-sided maximal operators on Orlicz and Lorentz spaces

- Mathematics
- 1998

In the paper, we characterize two weight weak and strong type inequalities for the fractional one-sided maximal operators on Lorentz and Orlicz space.

On weighted weak type norm inequalities for one-sided oscillatory singular integrals

- Mathematics
- 2011

We consider one sided weight classes of Muckenhoupt type and study the weighted weak type norm inequalities of a class of one sided oscillatory singular integrals with smooth kernel Introduction…