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BanachJ.Math.Anal.2(2008),no.2,9–15 HARDYINEQUALITYOFFRACTIONALORDER B J M A

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Banach J. Math. Anal. 2 (2008), no. 2, 9–15

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ournal of

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athematical

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nalysis ISSN: 1735-8787 (electronic)

http://www.math-analysis.org

HARDY INEQUALITY OF FRACTIONAL ORDER

PETR GURKA1 AND BOHUM´IR OPIC2∗

This paper is dedicated to Professor Josip E. Peˇcari´c Submitted by M. Abel

Abstract. We prove optimality of power-type weights in the Hardy inequality of fractional order.

1Department of Mathematics, Czech University of Agriculture, 165 21 Prague 6, Czech Republic.

E-mail address: [email protected]

2Mathematical Institute, Academy of Sciences of the Czech Republic, ˇZitn´a 25, 115 67 Prague 1, Czech Republic;

Department of Mathematics and Didactics of Mathematics, Pedagogical Fac- ulty, Technical University of Liberec, H´alkova 6, 46117 Liberec, Czech Repub- lic.

E-mail address: [email protected]

Date: Received: 29 February 2008; Accepted: 25 March 2008.

∗ Corresponding author.

2000Mathematics Subject Classification. 26D10.

Key words and phrases. Hardy inequality of fractional order, power-type weights.

The research was partly supported by grant no. 201/05/2033 of the Grant Agency of the Czech Republic and by the Institutional Research Plan no. AV0Z10190503 of the Academy of Sciences of the Czech Republic.

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