MATHEMATICA BOHEMICA, Vol. 124, No. 2–3, pp. 231-244 (1999)

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:

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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