Martingale operators and Hardy spaces generated by them

Ferenc Weisz

ArticleOriginal scientific text

Title

Martingale operators and Hardy spaces generated by them

Authors ¹

Affiliations

Department of Numerical Analysis, Eötvös Lorand University, Múzeum krt. 6-8, H-1088 Budapest, Hungary.

Abstract

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. Martingale inequalities between Hardy spaces generated by two different operators are considered. In particular, we obtain inequalities for the maximal function, for the q-variation and for the conditional q-variation. The duals of the Hardy spaces generated by these special operators are characterized.

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Title

Martingale operators and Hardy spaces generated by them

Affiliations

Abstract

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