# Martingale operators and Hardy spaces generated by them

Studia Mathematica (1995)

- Volume: 114, Issue: 1, page 39-70
- ISSN: 0039-3223

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topWeisz, Ferenc. "Martingale operators and Hardy spaces generated by them." Studia Mathematica 114.1 (1995): 39-70. <http://eudml.org/doc/216179>.

@article{Weisz1995,

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 $BMO_q$ 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.},

author = {Weisz, Ferenc},

journal = {Studia Mathematica},

keywords = {martingale operators; martingale Hardy spaces; BMO spaces; interpolation spaces; martingale inequalities; duals of the Hardy spaces; special operators},

language = {eng},

number = {1},

pages = {39-70},

title = {Martingale operators and Hardy spaces generated by them},

url = {http://eudml.org/doc/216179},

volume = {114},

year = {1995},

}

TY - JOUR

AU - Weisz, Ferenc

TI - Martingale operators and Hardy spaces generated by them

JO - Studia Mathematica

PY - 1995

VL - 114

IS - 1

SP - 39

EP - 70

AB - 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 $BMO_q$ 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.

LA - eng

KW - martingale operators; martingale Hardy spaces; BMO spaces; interpolation spaces; martingale inequalities; duals of the Hardy spaces; special operators

UR - http://eudml.org/doc/216179

ER -

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