Poincaré–Sobolev and isoperimetric inequalities, maximal functions, and half-space estimates for the gradient

Wheeden, Richard L.

Displaying similar documents to “Poincaré–Sobolev and isoperimetric inequalities, maximal functions, and half-space estimates for the gradient”

Superlinear equations, potential theory and weighted norm inequalities

Verbitsky, Igor E.

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Weighted norm inequalities for singular integral operators satisfying a variant of Hörmander's condition

R. Trujillo-González (2003)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we establish weighted norm inequalities for singular integral operators with kernel satisfying a variant of the classical Hörmander's condition.

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 $K (x, y) = k_{1} (x - A_{1} y) \dots k_{m} (x - A_{m} y),$ $k_{i} (x) = {Ω_{i} (x) / |x|}^{n / q_{i}}$ 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.

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, $0 < α < m n$ , $\vec{b} = (b_{1}, \dots, b_{m}) \in {BMO}^{m}$ . We give sufficient conditions on weights for the commutators of multilinear fractional integral operators $ℐ_{α}^{\vec{b}}$ 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...