Factorization of operators and weighted norm inequalities

García-Cuerva, José

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The boundedness, compactness and closedness of the range of weighted composition operators acting on weighted Lorentz spaces L(p,q,wdμ) for 1 < p ≤ ∞, 1 ≤ q ≤ ∞ are characterized.

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In this paper, we present some theorems on weighted approximation by two dimensional nonlinear singular integral operators in the following form: T λ ( f ; x , y ) = ∬ R 2 ( t − x , s − y , f ( t , s ) ) d s d t , ( x , y ) ∈ R 2 , λ ∈ Λ , $T_{λ} (f; x, y) = \underset{ℝ^{2}}{\int \int} (t - x, s - y, f (t, s)) d s d t, (x, y) \in ℝ^{2}, λ \in Λ,$ where Λ is a set of non-negative numbers with accumulation point λ0.

Weighted composition operators between a weighted-type space and the Hardy space on the unit ball

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J. Chabrowski, P. M. Girão (2001)

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