Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 211-223

HARDY AND HARDY–RELLICH TYPE INEQUALITIES WITH BESSEL PAIRS

Nguyen Lam

University of British Columbia, Department of Mathematics
and The Pacific Institute for the Mathematical Sciences
Vancouver, BC V6T1Z4, Canada; nlam 'at' math.ubc.ca

Abstract. Using the Bessel pairs in the sense of Ghoussoub and Moradifam [16], we provide the necessary and sufficient conditions on a pair of positive functions so that the Hardy type inequalities in the spirit of Badiale–Tarantello [3] hold. We also set up the requirements for a pair of potentials so that the Hardy–Rellich type inequalities with radial derivatives are valid.

2010 Mathematics Subject Classification: Primary 26D10, 35A23, 46E35.

Key words: Bessel pairs, Hardy inequalities, Hardy–Rellich inequalities, Heisenberg–Pauli–Weyl uncertainly principle, best constants.

Reference to this article: N. Lam: Hardy and Hardy–Rellich type inequalities with Bessel pairs. Ann. Acad. Sci. Fenn. Math. 43 (2018), 211-223.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4308