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Martingale operators and Hardy spaces generated by them

Ferenc Weisz (1995)

Studia Mathematica

Martingale Hardy spaces and BMO spaces generated by an operator T are investigated. An atomic decomposition of the space H p T is given if the operator T is predictable. We generalize the John-Nirenberg theorem, namely, we prove that the B M O q spaces generated by an operator T are all equivalent. The sharp operator is also considered and it is verified that the L p norm of the sharp operator is equivalent to the H p T norm. The interpolation spaces between the Hardy and BMO spaces are identified by the real method....

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