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On Entropy Bumps for Calderón-Zygmund Operators

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EN
Abstrakty
EN
We study twoweight inequalities in the recent innovative language of ‘entropy’ due to Treil-Volberg. The inequalities are extended to Lp, for 1 < p ≠ 2 < ∞, with new short proofs. A result proved is as follows. Let ℇ be a monotonic increasing function on (1,∞) which satisfy [...] Let σ and w be two weights on Rd. If this supremum is finite, for a choice of 1 < p < ∞, [...] then any Calderón-Zygmund operator T satisfies the bound [...]
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
otrzymano
2015-03-11
zaakceptowano
2015-05-19
online
2015-07-08
Twórcy
  • School of Mathematics, Georgia Institute of Technology, Atlanta GA 30332, USA
  • School of Mathematics, Georgia Institute of Technology, Atlanta GA 30332, USA
Bibliografia
  • [1] Cruz-Uribe, D., Pérez, C., Two-weight, weak-type norm inequalities for fractional integrals, Calderón-Zygmund operatorsand commutators. Indiana Univ. Math. J., 49, 2000, no. 2, 697–721. DOI:10.1512/iumj.2000.49.1795
  • [2] Cruz-Uribe, David, Reznikov, Alexander, Volberg, Alexander, Logarithmic bumpconditions and the two-weight boundednessof Calderón–Zygmund operators. Adv. Math., 255, 2014, 706–729. DOI:10.1016/j.aim.2014.01.016
  • [3] Ding, Shusen, Two-weight Caccioppoli inequalities for solutions of nonhomogeneous A-harmonic equations on Riemannianmanifolds. Proc. Amer. Math. Soc., 132, 2004, no. 8, 2367–2375. DOI:10.1090/S0002-9939-04-07347-2
  • [4] Hunt, Richard, Muckenhoupt, Benjamin, Wheeden, Richard, Weighted norm inequalities for the conjugate function andHilbert transform. Trans. Amer. Math. Soc., 176, 1973, 227–251.
  • [5] Hytönen, Tuomas P., The A2 theorem: remarks and complements. Contemp. Math., 612, Amer. Math. Soc., Providence, RI,2014, 91–106. DOI:10.1090/conm/612/12226
  • [6] Lacey, Michael T., On the Separated Bumps Conjecture for Calderon-Zygmund Operators . HokkaidoMath J, to appear, 2013,1310.3507
  • [7] Lacey, Michael T., An elementary proof of the A2 Bound. 2015, 1501.05818
  • [8] Hytönen, Tuomas P., Lacey, Michael T., Martikainen, Henri, Orponen, Tuomas, Reguera, Maria Carmen, Sawyer, Eric T.,Uriarte-Tuero, Ignacio, Weak and strong type estimates for maximal truncations of Calderón-Zygmund operators on Apweighted spaces. J. Anal. Math., 118, 2012, no. 1, 177–220. DOI:10.1007/s11854-012-0033-3
  • [9] Hytönen, Tuomas P., Lacey, Michael T., The Ap-A1 inequality for general Calderón-Zygmund operators. Indiana Univ. Math.J., 61, 2012, no. 6, 2041–2092. DOI:10.1512/iumj.2012.61.4777
  • [10] Hytönen, Tuomas, Pérez, Carlos, Sharp weighted bounds involving A1. Anal. PDE, 6, 2013, no. 4, 777–818.DOI:10.2140/apde.2013.6.777
  • [11] Hytönen, Tuomas, Pérez, Carlos, Treil, Sergei, Volberg, Alexander, Sharp weighted estimates for dyadic shifts and the A2conjecture. J. Reine Angew. Math., 687, 2014, 43–86. DOI:10.1515/crelle-2012-0047
  • [12] Lacey, Michael T., An Ap-A1 inequality for the Hilbert transform. Houston J. Math., 38, 2012, no. 3, 799–814.
  • [13] Lacey, Michael T., Petermichl, Stefanie, Reguera, Maria Carmen, Sharp A2 inequality for Haar shift operators. Math. Ann.,348, 2010, no. 1, 127–141. DOI:10.1007/s00208-009-0473-y
  • [14] Lacey, Michael T., Sawyer, Eric T., Uriarte-Tuero, Ignacio, Two Weight Inequalities for Discrete Positive Operators. 2009,Submitted, 0911.3437
  • [15] Lerner, Andrei K., On an estimate of Calderón-Zygmund operators by dyadic positive operators. J. Anal. Math., 121, 2013,141–161. DOI:10.1007/s11854-013-0030-1
  • [16] Lerner, Andrei K., A simple proof of the A2 conjecture. Int. Math. Res. Not. IMRN, 2013, no. 14, 3159–3170.
  • [17] Lerner, Andrei K., Mixed Ap-Ar inequalities for classical singular integrals and Littlewood-Paley operators. J. Geom. Anal.,23, 2013, no. 3, 1343–1354. DOI:10.1007/s12220-011-9290-0
  • [18] Lerner, Andrei K., Moen, Kabe, Mixed Ap-A1 estimates with one supremum. Studia Math., 219, 2013, no. 3, 247–267.DOI:10.4064/sm219-3-5
  • [19] Muckenhoupt, Benjamin, Weighted norm inequalities for the Hardy maximal function. Trans. Amer. Math. Soc., 165, 1972,207–226.
  • [20] Nazarov, Fedor, Reznikov, Alexander, Treil, Sergei, Volberg, ALexander, A Bellman function proof of the L2 bump conjecture.J. Anal. Math., 121, 2013, 255–277. DOI:10.1007/s11854-013-0035-9
  • [21] Neugebauer, C. J., title=Inserting Ap-weights, Proc. Amer. Math. Soc., 87, 1983, no. 4, 644–648. DOI:10.2307/2043351
  • [22] Pérez, C., Weighted norm inequalities for singular integral operators. J. London Math. Soc. (2), 49, 1994, no. 2, 296–308.DOI:10.1112/jlms/49.2.296
  • [23] Sawyer, Eric T., A characterization of a two-weight norm inequality for maximal operators. Studia Math., 75, 1982, no. 1,1–11.
  • [24] Sawyer, Eric T., A characterization of two weight norm inequalities for fractional and Poisson integrals. Trans. Amer. Math.Soc., 308, 1988, no. 2, 533–545. DOI:10.2307/2001090
  • [25] Treil, Sergei, Volberg, Alexander, Entropy conditions in two weight inequalities for singular integral operators. 1408.03852014,
  • [26] Zheng, Dechao, The distribution function inequality and products of Toeplitz operators and Hankel operators. J. Funct. Anal.,138, 1996, no. 2, 477–501. DOI:10.1006/jfan.1996.0073
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_conop-2015-0002
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