Conjugate index explained

p,q>1

are called conjugate indices (or Hölder conjugates) if

	1
	p

	1
	q

=1.

Formally, we also define

q=infty

as conjugate to

p=1

and vice versa.

Conjugate indices are used in Hölder's inequality, as well as Young's inequality for products; the latter can be used to prove the former. If

p,q>1

are conjugate indices, the spaces L^p and L^q are dual to each other (see L^p space).

References