Geodesic
Modular inequalities for the Hardy averaging operator
Mathematica Bohemica, Tome 124 (1999) no. 2-3, pp. 231-244

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MR Zbl
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.
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.
DOI : 10.21136/MB.1999.126254
Classification : 26A33, 26D05, 26D15, 46E30, 46M35
Keywords: Hardy inequality; modular inequality; weight functions 
Heinig, Hans P. Modular inequalities for the Hardy averaging operator. Mathematica Bohemica, Tome 124 (1999) no. 2-3, pp. 231-244. doi: 10.21136/MB.1999.126254
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[1] Maria J. Carro, Hans Heinig: Modular inequalities for the Calderón operator. Tohoku Math. J. To appear. | MR

[2] M. DeGuzmán: Real Variable Methods in Fourier analysis. Univ. Complutense de Madrid, Fac. Mat., 1977.

[3] P. Drábek H. P. Heinig A. Kufner: Higher dimensional Hardy inequality. Internat. Ser. Numer. Math. 123 (1997), 3-16. | MR

[4] G. H. Hardy J. E. Littlewood G. Pólya: Inequalities. Cambridge, 1934. | MR

[5] H. P. Heinig R. Kerman M. Krbec: Weighted exponential inequalities. Preprint, vol. 79, Math. Inst., Acad. Science, Praha, 1992, pp. 30. | MR

[6] Hans P. Heinig, Qinsheng Lai: Weighted modular inequalities for Hardy-type operators on monotone functions. Preprint. | MR

[7] Qinsheng Lai: Weighted modular inequalities for Hardy-type operators. J. London Math. Soc. To appear. | MR

[8] N. Levinson: Generalizations of an inequality of Hardy. Duke J. Math. 31 (1964), 389-394. | DOI | MR | Zbl

[9] B. Opic A. Kufner: Hardy type inequalities. Pitman Series 219, Harlow, 1990. | MR

[10] B. Opic P. Gurka: Weighted inequalities for geometric means. Proc. Arner. Math. Soc. 120 (1994), no. 3, 771-779. | DOI | MR

[11] E. Sawyer: Weighted inequalities for the two dimensional Hardy operator. Studia Math. 82 (1985), 1-16. | DOI | MR | Zbl

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