Let and be bilinear forms

and suppose that and are bounded in with bounds and . Then

where the series

is absolutely convergent, is called the faltung of and . is bounded in , and its bound does not exceed .

**References**

Hardy, G. H.; Littlewood, J. E.; and Pólya, G. *Inequalities, 2nd ed.* Cambridge,
England: Cambridge University Press, pp. 210-211, 1988.

© 1996-9

1999-05-26