Weighted bilinear Hardy inequalities. - Aguilar-Cañestro, María Isabel; Ortega-Salvador, Pedro; Ramírez Torreblanca, Consuelo (Elsevier, 2012)
We characterize the weights w, w1, w2 such that the weighted bilinear Hardy inequality b a x a f q x a g q w(x)dx 1q C b a f p1w1 1 p1 b a gp2 w2 1 p2 holds for all nonnegative functions f and g, with a positive constant C independent of f and g, for all possible values of q, p1 and p2 with 1 < q, p1, p2 <∞. We also characterize the good weights for the weighted bilinear n-dimensional Hardy inequality to hold.
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Keywords: Desigualdades (Matemáticas); Análisis matemático; Bilinear operators; Hardy operators; Weighted inequalities; Weights