Corpus ID: 237532593

Lower bound of the parabolic Hilbert commutator

@inproceedings{Oikari2021LowerBO,
  title={Lower bound of the parabolic Hilbert commutator},
  author={Tuomas Oikari},
  year={2021}
}
Answering a key point left open in the recent work of Bongers, Guo, Li and Wick [2], we provide the lower bound ‖b‖BMOγ(R2) . ‖[b,Hγ ]‖Lp(R2)→Lp(R2), where Hγ is the parabolic Hilbert transform. 

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References

SHOWING 1-10 OF 19 REFERENCES
Sparse domination of Hilbert transforms along curves
We obtain sharp sparse bounds for Hilbert transforms along curves in $\mathbb{R}^n$, and derive as corollaries weighted norm inequalities for such operators. The curves that we consider includeExpand
Off-diagonal estimates for commutators of bi-parameter singular integrals
We study the commutators $[b,T]$ of pointwise multiplications and bi-parameter Calderon-Zygmund operators and characterize their off-diagonal $L^{p_1}L^{p_2} \to L^{q_1}L^{q_2}$ boundedness in theExpand
Off-diagonal estimates for bilinear commutators
We find a minimal notion of non-degeneracy for bilinear singular integral operators T and identify testing conditions on the multiplying function b that characterize the L × L → L, 1 < p, q < ∞ and rExpand
Commutators of singular integrals revisited
We obtain a Bloom-type characterization of the two-weighted boundedness of iterated commutators of singular integrals. The necessity is established for a rather wide class of operators, providing aExpand
Off-diagonal estimates for bi-commutators
We study the bi-commutators $[T_1, [b, T_2]]$ of pointwise multiplication and Calderon-Zygmund operators, and characterize their $L^{p_1}L^{p_2} \to L^{q_1}L^{q_2}$ boundedness for severalExpand
Commutators of Hilbert transforms along monomial curves
The Hilbert transforms associated with monomial curves have a natural non-isotropic structure. We study the commutator of such Hilbert transforms and a symbol $b$ and prove the upper bound of thisExpand
The Unified Theory for the Necessity of Bounded Commutators and Applications
This paper gives unified criterions on the necessity of bounded commutators in linear and multilinear settings. Our results relax the restriction of Banach spaces in previous results to quasi-BanachExpand
Factorization theorems for Hardy spaces in several variables
The purpose of this paper is to extend to Hardy spaces in several variables certain well known factorization theorems on the unit disk. The extensions will be carried out for various spaces ofExpand
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, forExpand
Problems in harmonic analysis related to curvature
X \R(1 r\\ f /OO # / ( * ) --> e-*0 \B(e9 X)\ JB(t,x) for certain types of «-dimensional sets B(e9 x) shrinking to x as e -* 0. (\B(e9 x)\ is of course the Lebesgue measure of B(e9 x).) Some standardExpand
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