Entropy bump conditions for fractional maximal and integral operators

• Autorzy: Robert Rahm , Scott Spencer
• 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.

Słowa kluczowe

EN

Fractional integral operator; Fractional maximal operator; Weighted inequalities; Entropy bounds; Sparseoperator

• Wydawca: De Gruyter Open
• Czasopismo: Concrete Operators
• Rocznik: 2016
• Tom: 3
• Numer: 1
• Strony: 112-121

Daty

otrzymano

2016-03-26

zaakceptowano

2016-08-04

online

2016-08-30

Twórcy

autor

Robert Rahm

• School of Mathematics, Washington University in St. Louis, One Brookings Drive St. Louis, MO, USA

autor

Scott Spencer

• School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA, USA 30332

Bibliografia

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• [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
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• [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

Identyfikatory

DOI

10.1515/conop-2016-0013