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MATHEMATICA BOHEMICA, Vol. 124, No. 2–3, pp. 231-244 (1999)
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# Modular inequalities for the Hardy averaging operator

## Hans P. Heinig

* Hans P. Heinig*, Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S 4K1, e-mail: ` heinig@mcmail.CIS.McMaster.ca`

**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

**Full text of the article:**

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