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Displaying similar documents to “A two-weight estimate for a class of fractional integral operators with rough kernel.”

Weighted endpoint estimates for commutators of multilinear fractional integral operators

Xuefang Yan, Limei Xue, Wenming Li (2012)

Czechoslovak Mathematical Journal

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Let m be a positive integer, 0 < α < m n , b → = ( b 1 , ⋯ , b m ) ∈ BMO m . We give sufficient conditions on weights for the commutators of multilinear fractional integral operators ℐ α b → to satisfy a weighted endpoint inequality which extends the result in D. Cruz-Uribe, A. Fiorenza: Weighted endpoint estimates for commutators of fractional integrals, Czech. Math. J. 57 (2007), 153–160. We also give a weighted strong type inequality which improves the result in X. Chen, Q. Xue: Weighted estimates for a class of multilinear fractional...

Weighted inequalities for some integral operators with rough kernels

María Riveros, Marta Urciuolo (2014)

Open Mathematics

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In this paper we study integral operators with kernels K ( x , y ) = k 1 ( x - A 1 y ) ⋯ k m x - A m y , k i x = Ω i x Ω i x x x n n q i q i where Ωi: ℝn → ℝ are homogeneous functions of degree zero, satisfying a size and a Dini condition, A i are certain invertible matrices, and n/q 1 +…+n/q m = n−α, 0 ≤ α < n. We obtain the appropriate weighted L p-L q estimate, the weighted BMO and weak type estimates for certain weights in A(p, q). We also give a Coifman type estimate for these operators.