Marcinkiewicz interpolation theorem: Difference between revisions

Revision as of 19:07, 19 September 2018

Revision as of 16:37, 6 December 2018

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:<math>\lambda_f(t) = \omega\left\{x\in X\mid |f(x)| > t\right\}.</math>

Then ''f'' is called '''weak <math>L^1</math>''' if there exists a constant ''C'' such that the distribution function of ''f'' satisfies the following inequality for all ''t''&nbsp;>&nbsp;0:

:<math>\lambda_f(t)\leq \frac{C}{t}.</math>