Displaying similar documents to “Poincaré inequalities for powers and products of admissible weights.”

Smooth approximation in weighted Sobolev spaces

Tero Kilpeläinen (1997)

Commentationes Mathematicae Universitatis Carolinae

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We give necessary and sufficient conditions for the equality H = W in weighted Sobolev spaces. We also establish a Rellich-Kondrachov compactness theorem as well as a Lusin type approximation by Lipschitz functions in weighted Sobolev spaces.

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.