Displaying similar documents to “Endpoint estimates and weighted norm inequalities for commutators of fractional integrals.”

Sharp L p -weighted Sobolev inequalities

Carlos Pérez (1995)

Annales de l'institut Fourier

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We prove sharp weighted inequalities of the form ∫ R n | f ( x ) | p v ( x ) d x ≤ C ∫ R n | q ( D ) ( f ) ( x ) | p N ( v ) ( x ) d x where q ( D ) is a differential operator and N is a combination of maximal type operator related to q ( D ) and to p .

Weighted Orlicz space integral inequalities for the Hardy-Littlewood maximal operator

S. Bloom, R. Kerman (1994)

Studia Mathematica

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Necessary and sufficient conditions are given for the Hardy-Littlewood maximal operator to be bounded on a weighted Orlicz space when the complementary Young function satisfies Δ 2 . Such a growth condition is shown to be necessary for any weighted integral inequality to occur. Weak-type conditions are also investigated.

On the two-weight problem for singular integral operators

David Cruz-Uribe, Carlos Pérez (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We give A p type conditions which are sufficient for two-weight, strong ( p , p ) inequalities for Calderón-Zygmund operators, commutators, and the Littlewood-Paley square function g λ * . Our results extend earlier work on weak ( p , p ) inequalities in [13].

Weighted endpoint estimates for commutators of fractional integrals

David Cruz-Uribe, Alberto Fiorenza (2007)

Czechoslovak Mathematical Journal

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Given α , 0 < α < n , and b ∈ B M O , we give sufficient conditions on weights for the commutator of the fractional integral operator, [ b , I α ] , to satisfy weighted endpoint inequalities on ℝ n and on bounded domains. These results extend our earlier work [3], where we considered unweighted inequalities on ℝ n .