Commutators of singular integrals on spaces of homogeneous type

Gladis Pradolini; Oscar Salinas

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 1, page 75-93
  • ISSN: 0011-4642

Abstract

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In this work we prove some sharp weighted inequalities on spaces of homogeneous type for the higher order commutators of singular integrals introduced by R. Coifman, R. Rochberg and G. Weiss in Factorization theorems for Hardy spaces in several variables, Ann. Math. 103 (1976), 611–635. As a corollary, we obtain that these operators are bounded on L p ( w ) when w belongs to the Muckenhoupt’s class A p , p > 1 . In addition, as an important tool in order to get our main result, we prove a weighted Fefferman-Stein type inequality on spaces of homogeneous type, which we have not found previously in the literature.

How to cite

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Pradolini, Gladis, and Salinas, Oscar. "Commutators of singular integrals on spaces of homogeneous type." Czechoslovak Mathematical Journal 57.1 (2007): 75-93. <http://eudml.org/doc/31114>.

@article{Pradolini2007,
abstract = {In this work we prove some sharp weighted inequalities on spaces of homogeneous type for the higher order commutators of singular integrals introduced by R. Coifman, R. Rochberg and G. Weiss in Factorization theorems for Hardy spaces in several variables, Ann. Math. 103 (1976), 611–635. As a corollary, we obtain that these operators are bounded on $L^\{p\}(w)$ when $w$ belongs to the Muckenhoupt’s class $A_\{p\}$, $p>1$. In addition, as an important tool in order to get our main result, we prove a weighted Fefferman-Stein type inequality on spaces of homogeneous type, which we have not found previously in the literature.},
author = {Pradolini, Gladis, Salinas, Oscar},
journal = {Czechoslovak Mathematical Journal},
keywords = {commutators; spaces of homogeneous type; weights; commutators; spaces of homogeneous type; weights},
language = {eng},
number = {1},
pages = {75-93},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Commutators of singular integrals on spaces of homogeneous type},
url = {http://eudml.org/doc/31114},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Pradolini, Gladis
AU - Salinas, Oscar
TI - Commutators of singular integrals on spaces of homogeneous type
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 1
SP - 75
EP - 93
AB - In this work we prove some sharp weighted inequalities on spaces of homogeneous type for the higher order commutators of singular integrals introduced by R. Coifman, R. Rochberg and G. Weiss in Factorization theorems for Hardy spaces in several variables, Ann. Math. 103 (1976), 611–635. As a corollary, we obtain that these operators are bounded on $L^{p}(w)$ when $w$ belongs to the Muckenhoupt’s class $A_{p}$, $p>1$. In addition, as an important tool in order to get our main result, we prove a weighted Fefferman-Stein type inequality on spaces of homogeneous type, which we have not found previously in the literature.
LA - eng
KW - commutators; spaces of homogeneous type; weights; commutators; spaces of homogeneous type; weights
UR - http://eudml.org/doc/31114
ER -

References

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