The best constant in the Davis inequality for the expectation of the martingale square function

@inproceedings{Burkholder2002TheBC,
  title={The best constant in the Davis inequality for the expectation of the martingale square function},
  author={Donald L. Burkholder},
  year={2002}
}
A method is introduced for the simultaneous study of the square function and the maximal function of a martingale that can yield sharp norm inequalities between the two. One application is that the expectation of the square function of a martingale is not greater than √ 3 times the expectation of the maximal function. This gives the best constant for one side of the Davis two-sided inequality. The martingale may take its values in any real or complex Hilbert space. The elementary discrete-time… CONTINUE READING

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