Entropy bump conditions for fractional maximal and integral operators

Robert Rahm; Scott Spencer

Concrete Operators (2016)

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

Abstract

top
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.

How to cite

top

Robert 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. [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. [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. [3] Cruz-Uribe, David, Two weight norm inequalities for fractional integral operators and commutators, 2015, http://arxiv.org/abs/1412.4157  
  4. [4] Duren, Peter L., Extension of a theorem of Carleson, Bull. Amer. Math. Soc., 75, 1969, 143–146  Zbl0184.30503
  5. [5] Hytönen, Tuomas P., The A2 Theorem: Remarks and Complements, 2012, http://www.arxiv.org/abs/1212.3840  
  6. [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. [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. [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. [9] Lacey, Michael T., Spencer, Scott, On Entropy Bounds for Calderón–Zygmund Operators, 2, 2015, 47–52  Zbl1333.42021
  10. [10] Moen, Kabe, Sharp weighted bounds without testing or extrapolation, Arch. Math. (Basel), 99, 2012, 5, 457–466 [WoS] Zbl1266.42037
  11. [11] Muckenhoupt, Benjamin, Wheeden, Richard, Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc., 192, 1974, 249–258  Zbl0226.44007
  12. [12] Neugebauer, C. J., Inserting Ap-weights, Proc. Amer. Math. Soc., 87, 1983, 4, 644–648  Zbl0521.42019
  13. [13] Pérez, Carlos, Two weighted inequalities for potential and fractional type maximal operators, Indiana Univ. Math. J., 43, 1994, 2, 31–44  
  14. [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. [15] Rochberg, Richard, NWO sequences, weighted potential operators, and Schrödinger eigenvalues, Duke Math. J., 72, 1993, 1, 187–215  
  16. [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. [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. [18] Treil, Sergei, Volberg, Alexander, Entropy conditions in two weight inequalities for singular integral operators, Adv. Math., 301, 2016, 499–548  Zbl06620627

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.