• Corpus ID: 222133950

Quantitative John-Nirenberg inequalities at different scales

@article{MartinezPerales2020QuantitativeJI,
  title={Quantitative John-Nirenberg inequalities at different scales},
  author={Javier C. Mart'inez-Perales and Ezequiel Rela and Israel P. Rivera-R'ios},
  journal={arXiv: Classical Analysis and ODEs},
  year={2020}
}
We provide an abstract estimate of the form \[ \|f-f_{Q,\mu}\|_{X \left(Q,\frac{\mathrm{d} \mu}{Y(Q)}\right)}\leq c(\mu,Y)\psi(X)\|f\|_{\mathrm{BMO}(\mathrm{d}\mu)} \] for all cubes $Q$ in $\mathbb{R}^n$ and every function $f\in \mathrm{BMO}(\mathrm{d}\mu)$, where $\mu$ is a doubling measure in $\mathbb{R}^n$, $Y$ is some positive functional defined on cubes, $\|\cdot \|_{X \left(Q,\frac{\mathrm{d} w}{w(Q)}\right)}$ is a sufficiently good quasi-norm and $c(\mu,Y)$ and $\psi(X)$ are positive… 

References

SHOWING 1-10 OF 24 REFERENCES
FUNCTIONS OF BOUNDED MEAN OSCILLATION
$BMO$, the space of functions of bounded mean oscillation, was first introduced by F. John and L. Nirenberg in 1961. It became a focus of attention when C. Fefferman proved that $BMO$ is the dual of
The L-to-L boundedness of commutators with applications to the Jacobian operator
  • T. Hytonen
  • Mathematics
    Journal de Mathématiques Pures et Appliquées
  • 2021
Supplying the missing necessary conditions, we complete the characterisation of the $L^p\to L^q$ boundedness of commutators $[b,T]$ of pointwise multiplication and Calder\'on-Zygmund operators, for
Degenerate Poincaré–Sobolev inequalities
  • C. Pérez, E. Rela
  • Mathematics
    Transactions of the American Mathematical Society
  • 2019
We study weighted Poincaré and Poincaré-Sobolev type inequalities with an explicit analysis on the dependence on the Ap constants of the involved weights. We obtain inequalities of the form ( 1 w(Q)
One and two weight norm inequalities for Riesz potentials
We consider weighted norm inequalities for the Riesz potentials $I_\alpha$, also referred to as fractional integral operators. First we prove mixed $A_p$-$A_\infty$ type estimates in the spirit of
COMPARISON OF TWO WEAK VERSIONS OF THE ORLICZ SPACES
In this work two versions of weak Orlicz spaces that appear in the literature, MA and MA, are analyzed. One of those include the weak Lebesgue spaces for 1 :5 p < 00, while the other version gives
On the two-weight problem for singular integral operators
We give $A_p$ type conditions which are sufficient for two-weight, strong $(p,p)$ inequalities for Calderon-Zygmund operators, commutators, and the Littlewood-Paley square function $g^*_\lambda $.
Fourier analysis
Fourier series allow you to expand a function on a finite interval as an infinite series of trigonometric functions. What if the interval is infinite? That's the subject of this chapter. Instead of a
A note on generalized Poincaré-type inequalities with applications to weighted improved Poincaré-type inequalities
The main result of this paper supports a conjecture by C. Perez and E. Rela about a very recent result of theirs on self-improving theory. Also, we extend the conclusions of their theorem to the
Two-weight, weak-type norm inequalities for fractional integrals, Calderon-Zygmund operators and commutators
We give Ap-type conditions which are sucient for the two-weight, weak-type (p,p) inequalities for fractional integral operators, Calderon-Zygmund operators and commutators. For fractional integral
Operator theory: Advances and applications
Edited by Joseph A. Ball (Blacksburg, VA, USA) Harry Dym (Rehovot, Israel) Marinus A. Kaashoek (Amsterdam, The Netherlands) Heinz Langer (Vienna, Austria) Christiane Tretter (Bern, Switzerland)
...
1
2
3
...