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A criterion on oscillation and variation for the commutators of singular integral operators
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Feng Liu
Published/Copyright:
July 24, 2012
Abstract
This paper gives a criterion on the weighted norm estimates of the oscillatory and variation operators for the commutators of Calderón–Zygmund singular integrals in dimension 1. As applications, the weighted Lp-boundedness of the oscillation operators and the ρ-variation operators for commutators of the Hilbert transform and the Hermitian Riesz transform are obtained. In addition, the corresponding results for the λ-jump operators and the numbers of up-crossings associated with these operators are also given.
Keywords: Oscillation; variation; commutators; Hilbert transform; Hermite Riesz transform; Calderón–Zygmund operators
Funding source: NNSF of China
Award Identifier / Grant number: 11071200
Funding source: NSF of Fujian Province of China
Award Identifier / Grant number: 2010J01013
The authors would like to thank the referee for his/her invaluable comments and suggestions.
Received: 2012-2-27
Revised: 2012-6-18
Published Online: 2012-7-24
Published in Print: 2015-1-1
© 2015 by De Gruyter
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Keywords for this article
Oscillation;
variation;
commutators;
Hilbert transform;
Hermite Riesz transform;
Calderón–Zygmund operators
Articles in the same Issue
- Frontmatter
- On the character degrees of Sylow p-subgroups of Chevalley groups G(pf) of type E
- Achievable sets in ℤn
- A criterion on oscillation and variation for the commutators of singular integral operators
- Some 𝐇1𝔉-groups with unbounded torsion and a conjecture of Kropholler and Mislin
- Goodwillie calculus and Whitehead products
- Computing Borel's regulator
- Applications of a transcendence criterion for reciprocal sums of binary linear recurrences
- BSDE and generalized Dirichlet forms: The infinite dimensional case
- Faithful representations of infinite-dimensional nilpotent Lie algebras
- Locally finitely presented categories with no flat objects
- A common generalization of metric, ultrametric and topological fixed point theorems
- Correction to A common generalization of metric, ultrametric and topological fixed point theorems [Forum Math. 27 (2015), 303–327]
- Erdős–Rényi graph, Szemerédi–Trotter type theorem, and sum-product estimates over finite rings
- Minimal support results for Schrödinger equations
- Dynamics for the focusing, energy-critical nonlinear Hartree equation
- A fixed point theorem for Lie groups acting on buildings and applications to Kac–Moody theory
- On effective determination of Maass forms from central values of Rankin–Selberg L-function
- On embedding left-ordered groups into division rings
- Conservation property of symmetric jump-diffusion processes
- Irreducible representations of Leavitt path algebras
- Commutators of elements of coprime orders in finite groups
- Endoscopy and the transfer from GSp(4) to GL(4)
- Cycles in Leavitt path algebras by means of idempotents
- On volumes determined by subsets of Euclidean space
