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

doi:10.1016/S0252-9602(17)30119-4

Abstract

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.

Key words: Morrey spaces,Banach function space, block spaces,Doob's inequality, Burkholder-Gundy inequality, martingale transform, Davis'decomposition, martingale

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.

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