On weighted multidimensional embeddings for monotone functions - Barza, Sorina; Persson, Lars-Erik; Stepanov, Vladimir D. (Mathematica Scandinavica, 2001)
We characterize the inequality 7817 (_R^N_+ f^q u)^1/q ≤ C (_R^N_+ f^p v )^1/p, 0<q ,p <∞, 7817 for monotone functions f≥ 0 and nonnegative weights u and v. The case q < p is new and the case 0<p≤ q <∞ is extended to a modular inequality with N- functions. A remarkable fact concerning the calculation of C is pointed out.