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2016 | 3 | 1 | 112-121
Tytuł artykułu

Entropy bump conditions for fractional maximal and integral operators

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We investigate weighted inequalities for fractional maximal operators and fractional integral operators.We work within the innovative framework of “entropy bounds” introduced by Treil–Volberg. Using techniques developed by Lacey and the second author, we are able to efficiently prove the weighted inequalities.
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
1
Strony
112-121
Opis fizyczny
Daty
otrzymano
2016-03-26
zaakceptowano
2016-08-04
online
2016-08-30
Twórcy
autor
  • School of Mathematics, Washington University in St. Louis, One Brookings Drive St. Louis, MO, USA
  • School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA, USA 30332
Bibliografia
  • [1] Cruz-Uribe, David, Moen, Kabe, A fractional Muckenhoupt-Wheeden theorem and its consequences, Integral Equations Operator Theory, 76, 2013, 3, 421–446
  • [2] Cruz-Uribe, David, Moen, Kabe, One and two weight norm inequalities for Riesz potentials, Illinois J. Math., 57, 2013, 1, 295–323
  • [3] Cruz-Uribe, David, Two weight norm inequalities for fractional integral operators and commutators, 2015, http://arxiv.org/abs/1412.4157
  • [4] Duren, Peter L., Extension of a theorem of Carleson, Bull. Amer. Math. Soc., 75, 1969, 143–146
  • [5] Hytönen, Tuomas P., The A2 Theorem: Remarks and Complements, 2012, http://www.arxiv.org/abs/1212.3840
  • [6] Lerner, Andrei K., A pointwise estimate for the local sharp maximal function with applications to singular integrals, Bull. Lond. Math. Soc., 42, 2010, 5, 843–856 [WoS]
  • [7] Lacey, Michael T., Moen, Kabe, Pérez, Carlos, Torres, Rodolfo H., Sharp weighted bounds for fractional integral operators, J. Funct. Anal., 259, 2010, 5, 1073–1097 [WoS]
  • [8] Lacey, Michael T., Sawyer, Eric T., Uriarte-Tuero, Ignacio, Two Weight Inequalities for Discrete Positive Operators, 2009, http://arxiv.org/abs/0911.3437
  • [9] Lacey, Michael T., Spencer, Scott, On Entropy Bounds for Calderón–Zygmund Operators, 2, 2015, 47–52
  • [10] Moen, Kabe, Sharp weighted bounds without testing or extrapolation, Arch. Math. (Basel), 99, 2012, 5, 457–466 [WoS]
  • [11] Muckenhoupt, Benjamin, Wheeden, Richard, Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc., 192, 1974, 249–258
  • [12] Neugebauer, C. J., Inserting Ap-weights, Proc. Amer. Math. Soc., 87, 1983, 4, 644–648
  • [13] Pérez, Carlos, Two weighted inequalities for potential and fractional type maximal operators, Indiana Univ. Math. J., 43, 1994, 2, 31–44
  • [14] Pérez, Carlos, On sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator between weighted Lp-spaces with different weights, Proc. London Math. Soc. (3), 71, 1995, 1, 135–157
  • [15] Rochberg, Richard, NWO sequences, weighted potential operators, and Schrödinger eigenvalues, Duke Math. J., 72, 1993, 1, 187–215
  • [16] Sawyer, Eric T., A characterization of two weight norm inequalities for fractional and Poisson integrals, Trans. Amer. Math. Soc., 308, 1988, 2, 533–545
  • [17] Sawyer, Eric T., A characterization of a two-weight norm inequality for maximal operators, Studia Math., 75, 1982, 1, 1–11
  • [18] Treil, Sergei, Volberg, Alexander, Entropy conditions in two weight inequalities for singular integral operators, Adv. Math., 301, 2016, 499–548
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_conop-2016-0013
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