Weighted Inequalities for Monotone Functions
Copyright policy )Weighted Inequalities for Monotone Functions
AbstractWeighted norm inequalities are investigated by giving an extension of the Riesz convexity theorem to semi‐linear operators on monotone functions. Several properties of the classes B(p, n) and C(p, n) introduced by Neugebauer in [13] are given. In particular, we characterize the weight pairs w, v for which \documentclass{article}\pagestyle{empty}\begin{document}$ \int\limits_0^\infty {f(x)^p w(x)dx \le C \int\limits_0^\infty {({\textstyle{1 \over x}}\int\limits_0^x f)^p } v(x) dx,} $\end{document} for nondecreasing functions f and 1 ≦ p < ∞.
weighted inequalities, monotone functions, Maximal functions, Littlewood-Paley theory, Interpolation between normed linear spaces, weighted norm inequalities, Inequalities involving derivatives and differential and integral operators, Riesz convexity theorem, Monotonic functions, generalizations, reverse Hardy-type weighted inequalities
weighted inequalities, monotone functions, Maximal functions, Littlewood-Paley theory, Interpolation between normed linear spaces, weighted norm inequalities, Inequalities involving derivatives and differential and integral operators, Riesz convexity theorem, Monotonic functions, generalizations, reverse Hardy-type weighted inequalities
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