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1. Boundedness of fractional operators in weighted variable exponent spaces with non doubling measures

Creator:
Gorosito, Osvaldo, Pradolini, Gladis, and Salinas, Oscar
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
variable exponent, weighted spaces, and non doubling measures
Language:
English
Description:
In the context of variable exponent Lebesgue spaces equipped with a lower Ahlfors measure we obtain weighted norm inequalities over bounded domains for the centered fractional maximal function and the fractional integral operator.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Commutators of singular integrals on spaces of homogeneous type

Creator:
Pradolini, Gladis and Salinas, Oscar
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
commutators, spaces of homogeneous type, and weights
Language:
English
Description:
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public