On optimal parameters involved with two-weighted estimates of commutators of singular and fractional operators with Lipschitz symbols

Gladis Pradolini; Jorgelina Recchi

Czechoslovak Mathematical Journal (2023)

  • Volume: 73, Issue: 3, page 733-754
  • ISSN: 0011-4642

Abstract

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We prove two-weighted norm estimates for higher order commutator of singular integral and fractional type operators between weighted L p and certain spaces that include Lipschitz, BMO and Morrey spaces. We also give the optimal parameters involved with these results, where the optimality is understood in the sense that the parameters defining the corresponding spaces belong to a certain region out of which the classes of weights are satisfied by trivial weights. We also exhibit pairs of nontrivial weights in the optimal region satisfying the conditions required.

How to cite

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Pradolini, Gladis, and Recchi, Jorgelina. "On optimal parameters involved with two-weighted estimates of commutators of singular and fractional operators with Lipschitz symbols." Czechoslovak Mathematical Journal 73.3 (2023): 733-754. <http://eudml.org/doc/299106>.

@article{Pradolini2023,
abstract = {We prove two-weighted norm estimates for higher order commutator of singular integral and fractional type operators between weighted $L^p$ and certain spaces that include Lipschitz, BMO and Morrey spaces. We also give the optimal parameters involved with these results, where the optimality is understood in the sense that the parameters defining the corresponding spaces belong to a certain region out of which the classes of weights are satisfied by trivial weights. We also exhibit pairs of nontrivial weights in the optimal region satisfying the conditions required.},
author = {Pradolini, Gladis, Recchi, Jorgelina},
journal = {Czechoslovak Mathematical Journal},
keywords = {fractional operator; singular integral operator; commutator; weight},
language = {eng},
number = {3},
pages = {733-754},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On optimal parameters involved with two-weighted estimates of commutators of singular and fractional operators with Lipschitz symbols},
url = {http://eudml.org/doc/299106},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Pradolini, Gladis
AU - Recchi, Jorgelina
TI - On optimal parameters involved with two-weighted estimates of commutators of singular and fractional operators with Lipschitz symbols
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 3
SP - 733
EP - 754
AB - We prove two-weighted norm estimates for higher order commutator of singular integral and fractional type operators between weighted $L^p$ and certain spaces that include Lipschitz, BMO and Morrey spaces. We also give the optimal parameters involved with these results, where the optimality is understood in the sense that the parameters defining the corresponding spaces belong to a certain region out of which the classes of weights are satisfied by trivial weights. We also exhibit pairs of nontrivial weights in the optimal region satisfying the conditions required.
LA - eng
KW - fractional operator; singular integral operator; commutator; weight
UR - http://eudml.org/doc/299106
ER -

References

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  9. Muckenhoupt, B., Wheeden, R. L., 10.4064/sm-54-3-221-237, Stud. Math. 54 (1976), 221-237. (1976) Zbl0318.26014MR0399741DOI10.4064/sm-54-3-221-237
  10. Pradolini, G., A class of pairs of weights related to the boundedness of the fractional integral operator between L p and Lipschitz spaces, Commentat. Math. Univ. Carol. 42 (2001), 133-152. (2001) Zbl1055.42015MR1825378
  11. Pradolini, G., Two-weighted norm inequalities for the fractional integral operator between L p and Lipschitz spaces, Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 41 (2001), 147-169. (2001) Zbl0997.42010MR1876717
  12. Pradolini, G., Ramos, W., Recchi, J., 10.1007/s13348-020-00287-1, Collect. Math. 72 (2021), 229-259. (2021) Zbl1457.42029MR4204587DOI10.1007/s13348-020-00287-1
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