# Entropy bump conditions for fractional maximal and integral operators

Concrete Operators (2016)

- Volume: 3, Issue: 1, page 112-121
- ISSN: 2299-3282

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topRobert Rahm, and Scott Spencer. "Entropy bump conditions for fractional maximal and integral operators." Concrete Operators 3.1 (2016): 112-121. <http://eudml.org/doc/286776>.

@article{RobertRahm2016,

abstract = {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.},

author = {Robert Rahm, Scott Spencer},

journal = {Concrete Operators},

keywords = {Fractional integral operator; Fractional maximal operator; Weighted inequalities; Entropy bounds; Sparse
operator; fractional maximal operator; fractional integral operator; weighted inequalities; entropy bounds; sparse operator},

language = {eng},

number = {1},

pages = {112-121},

title = {Entropy bump conditions for fractional maximal and integral operators},

url = {http://eudml.org/doc/286776},

volume = {3},

year = {2016},

}

TY - JOUR

AU - Robert Rahm

AU - Scott Spencer

TI - Entropy bump conditions for fractional maximal and integral operators

JO - Concrete Operators

PY - 2016

VL - 3

IS - 1

SP - 112

EP - 121

AB - 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.

LA - eng

KW - Fractional integral operator; Fractional maximal operator; Weighted inequalities; Entropy bounds; Sparse
operator; fractional maximal operator; fractional integral operator; weighted inequalities; entropy bounds; sparse operator

UR - http://eudml.org/doc/286776

ER -

## References

top- [1] Cruz-Uribe, David, Moen, Kabe, A fractional Muckenhoupt-Wheeden theorem and its consequences, Integral Equations Operator Theory, 76, 2013, 3, 421–446 Zbl1275.42029
- [2] Cruz-Uribe, David, Moen, Kabe, One and two weight norm inequalities for Riesz potentials, Illinois J. Math., 57, 2013, 1, 295–323 Zbl1297.42022
- [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 Zbl0184.30503
- [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] Zbl1203.42023
- [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] Zbl1196.42014
- [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 Zbl1333.42021
- [10] Moen, Kabe, Sharp weighted bounds without testing or extrapolation, Arch. Math. (Basel), 99, 2012, 5, 457–466 [WoS] Zbl1266.42037
- [11] Muckenhoupt, Benjamin, Wheeden, Richard, Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc., 192, 1974, 249–258 Zbl0226.44007
- [12] Neugebauer, C. J., Inserting Ap-weights, Proc. Amer. Math. Soc., 87, 1983, 4, 644–648 Zbl0521.42019
- [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 Zbl0829.42019
- [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 Zbl0665.42023
- [17] Sawyer, Eric T., A characterization of a two-weight norm inequality for maximal operators, Studia Math., 75, 1982, 1, 1–11 Zbl0508.42023
- [18] Treil, Sergei, Volberg, Alexander, Entropy conditions in two weight inequalities for singular integral operators, Adv. Math., 301, 2016, 499–548 Zbl06620627

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