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Keywords:
Hardy inequality; modular inequality; weight functions
Hardy inequality; modular inequality; weight functions
Summary:
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.
References:
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