Marcinkiewicz interpolation theorem: Difference between revisions

Revision as of 03:30, 9 December 2014

Revision as of 03:20, 25 March 2016

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The constants δ and γ can also be given for ''q'' = ∞ by passing to the limit.

A version of the theorem also holds more generally if ''T'' is only assumed to be a [[quasilinear]] operator. That is, there exists a constant ''C'' > 0 such that ''T'' satisfies

:<math>|T(f+g)(x)| \le C(|Tf(x)|+|Tg(x)|)</math>

for [[almost everywhere|almost every]] ''x''. The theorem holds precisely as stated, except with γ replaced by