Sharp weighted bounds without testing or extrapolation
- Kabe Moen
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
We give a short proof of the sharp weighted bound for sparse operators that holds for all p,1 < p < ∞. By recent developments this implies the bounds hold for any Calderón–Zygmund operator. The novelty of our approach is that we avoid two techniques that are present in other proofs: two weight inequalities and extrapolation. Our techniques are applicable to fractional integral operators as well.
- Bennett, C., Sharpley, R. (1988) Interpolation of Operators. Academic Press, New York
- Cruz-Uribe, D., Martell, J.M., Pérez, C. (2012) Sharp weighted estimates for classical operators. Adv. Math. 229: pp. 408-441 CrossRef
- D. Cruz-Uribe and K. Moen One and two weight norm inequalities for Riesz potentials, accepted in Illinois J. Math.
- L. Grafakos, Modern Fourier Analysis, Springer-Verlag, Graduate Texts in Mathematics 250, Second Edition 2008.
- Hytönen, T. (2012) The sharp weighted bound for general Calderon-Zygmund operators. Ann. of Math. 175: pp. 1473-1506 CrossRef
- T. Hytönen and M. Lacey, The A p -A ∞ inequality for general Calderón–Zygmund operators, Indiana Univ. Math. J. to appear.
- T. Hytönen et al., Weak and strong type estimates for maximal truncations of Calderón-Zygmund operators on A p weighted spaces, J Anal. Math. to appear.
- T. Hytönen, M. Lacey, and C. Pérez, Non-probabilistic proof of the A 2 theorem, and sharp weighted bounds for the q-variation of singular integrals, preprint (2012).
- T. Hytönen and F. Nazarov, The local Tb theorem with rough test functions, preprint.
- T. Hytönen and C. Pérez, Sharp weighted bounds involving A ∞ , Anal. PDE. to appear.
- T. P. Hytönen et al., Sharp weighted estimates of the dyadic shifts and A 2 conjecture, J. Reine Angew. Math. to appear.
- Lacey, M. (2010) Sharp weighted bounds for fractional integral operators. J. Func. Anal. 259: pp. 1073-1097 CrossRef
- Lacey, M., Petermichl, S. (2010) Reguera M. Sharp A 2 inequality for Haar shift operators. Math. Annalen 348: pp. 127-141 CrossRef
- A. Lerner Mixed A p -A r inequalities for classical singular integrals and Littlewood-Paley operators, J. Geom. Anal. to appear.
- A. Lerner, On an estimate of Calderón-Zygmund operators by dyadic positive operators, J. Anal. Math. to appear.
- A. Lerner, A simple proof of the A 2 conjecture, Int. Math. Res. Not., to appear.
- Moen, K. (2009) Sharp one-weight and two-weight bounds for maximal operators. Studia Math. 194: pp. 163-180 CrossRef
- Pérez, C. (1994) Two weighted inequalities for Potential and Fractional Type Maximal Operators. Indiana Univ. Math. J. 43: pp. 1-28 CrossRef
- Petermichl, S. (2007) The sharp bound for the Hilbert transform in weighted Lebesgue spaces in terms of the classical A p characteristic. Amer. J. Math. 129: pp. 1355-1375 CrossRef
- Petermichl, S., Volberg, A. (2002) Heating of the Ahlfors-Beurling operator: weakly quasiregular maps on the plane are quasiregular. Duke Math. J. 112: pp. 281-305 CrossRef
- Sawyer, E., Wheeden, R. (1992) Weighted inequalities for fractional integrals on euclidean and homogeneous spaces. Amer. J. Math. 114: pp. 813-874 CrossRef
- Sharp weighted bounds without testing or extrapolation
Archiv der Mathematik
Volume 99, Issue 5 , pp 457-466
- Cover Date
- Print ISSN
- Online ISSN
- SP Birkhäuser Verlag Basel
- Additional Links
- Calderón–Zygmund operators
- Riesz potentials
- A p weights
- Kabe Moen (1)
- Author Affiliations
- 1. Department of Mathematics, University of Alabama, Tuscaloosa, AL, 35487-0350, USA