Let Xt be a continuous process and suppose there exists such that for all t, Let Prove that there exists a depending only on K such that This is sometimes called the John–Nirenberg inequality...

Let X_t
be a continuous process and suppose there exists

such that for all t,

Let

Prove that there exists a depending only on K such that

This is sometimes called the John–Nirenberg inequality after the inequality of the same name in analysis.