Hardy's inequality is an inequality in mathematics, named after G. H. Hardy. It states that if is a sequence of non-negative real numbers which is not identically zero, then for every real number p > 1 one has
Hardy's inequality was first published and proved (at least the discrete version with a worse constant) in 1920 in a note by Hardy. The original formulation was in an integral form slightly different from the above.
- Hardy, G. H. (1920). "Note on a theorem of Hilbert". Mathematische Zeitschrift 6 (3–4): 314–317. doi:10.1007/BF01199965.
- Hardy, G. H.; Littlewood. J.E.; Pólya, G. (1952). Inequalities, 2nd ed. Cambridge University Press. ISBN 0-521-35880-9.
- Kufner, Alois; Persson, Lars-Erik (2003). Weighted inequalities of Hardy type. World Scientific Publishing. ISBN 981-238-195-3.