Martingale operators and Hardy spaces generated by them

Weisz, Ferenc

Weisz, Ferenc

Studia Mathematica, Tome 113 (1995), p. 39-70 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Publié le : 1995-01-01

Zbl 0822.60043

EUDML-ID : urn:eudml:doc:216179

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     title = {Martingale operators and Hardy spaces generated by them},
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     volume = {113},
     year = {1995},
     pages = {39-70},
     zbl = {0822.60043},
     language = {en},
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Weisz, Ferenc. Martingale operators and Hardy spaces generated by them. Studia Mathematica, Tome 113 (1995) pp. 39-70. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv114i1p39bwm/

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