Articles

DOOB'S INEQUALITY, BURKHOLDER-GUNDY INEQUALITY AND MARTINGALE TRANSFORMS ON MARTINGALE MORREY SPACES

  • Kwok-Pun HO
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  • Department of Mathematics and Information Technology, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, Hong Kong, China

Received date: 2016-12-23

  Revised date: 2017-04-26

  Online published: 2018-02-25

Abstract

We introduce the martingale Morrey spaces built on Banach function spaces. We establish the Doob's inequality, the Burkholder-Gundy inequality and the boundedness of martingale transforms for our martingale Morrey spaces. We also introduce the martingale block spaces. By the Doob's inequality on martingale block spaces, we obtain the Davis' decompositions for martingale Morrey spaces.

Cite this article

Kwok-Pun HO . DOOB'S INEQUALITY, BURKHOLDER-GUNDY INEQUALITY AND MARTINGALE TRANSFORMS ON MARTINGALE MORREY SPACES[J]. Acta mathematica scientia, Series B, 2018 , 38(1) : 93 -109 . DOI: 10.1016/S0252-9602(17)30119-4

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