Alejandro García del Amo Jiménez
In this note, several properties of the class $C(p, n)$ introduced by Neugebauer in [10] are given. In particular we characterize the weight pairs $w, v$ for which $$\int^\infty_0 f(x)^pw(x)dx\leq C\int^\infty_0\bigg(\frac{1}{x}\int^x_0 f\bigg)^p v(x)dx$$ for nondecreasing functions $f$ and $1\leq p <\infty$.
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