Abstract: If $P$ is the Hardy averaging operator—or some of its generalizations, then weighted modular inequalities of the form $$\int u \phi(Pf) \leq C\int v \phi(f)$$ are established for a general class of functions $\phi$. Modular inequalities for the two- and higher dimensional Hardy averaging operator are also given.
Keywords: Hardy inequality, modular inequality, weight functions
Classification (MSC2000): 26D15, 46E30, 46M35, 26A33
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