BMO and commutators of martingale transforms

Svante Janson

Annales de l'institut Fourier (1981)

  • Volume: 31, Issue: 1, page 265-270
  • ISSN: 0373-0956

Abstract

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The commutator of multiplication by a function and a martingale transform of a certain type is a bounded operator on , , if and only if the function belongs to BMO. This is a martingale version of a result by Coifman, Rochberg and Weiss.

How to cite

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Janson, Svante. "BMO and commutators of martingale transforms." Annales de l'institut Fourier 31.1 (1981): 265-270. <http://eudml.org/doc/74487>.

@article{Janson1981,
abstract = {The commutator of multiplication by a function and a martingale transform of a certain type is a bounded operator on $L^p$, $1&lt; p&lt; \infty $, if and only if the function belongs to BMO. This is a martingale version of a result by Coifman, Rochberg and Weiss.},
author = {Janson, Svante},
journal = {Annales de l'institut Fourier},
keywords = {commutators of martingales transforms; d-adic martingales},
language = {eng},
number = {1},
pages = {265-270},
publisher = {Association des Annales de l'Institut Fourier},
title = {BMO and commutators of martingale transforms},
url = {http://eudml.org/doc/74487},
volume = {31},
year = {1981},
}

TY - JOUR
AU - Janson, Svante
TI - BMO and commutators of martingale transforms
JO - Annales de l'institut Fourier
PY - 1981
PB - Association des Annales de l'Institut Fourier
VL - 31
IS - 1
SP - 265
EP - 270
AB - The commutator of multiplication by a function and a martingale transform of a certain type is a bounded operator on $L^p$, $1&lt; p&lt; \infty $, if and only if the function belongs to BMO. This is a martingale version of a result by Coifman, Rochberg and Weiss.
LA - eng
KW - commutators of martingales transforms; d-adic martingales
UR - http://eudml.org/doc/74487
ER -

References

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  1. [1] R.R. COIFMAN, R. ROCHBERG and G. WEISS, Factorization theorems for Hardy spaces in several variables, Ann. Math., 103 (1976), 611-635. Zbl0326.32011MR54 #843
  2. [2] C. FEFFERMAN and E.M. STEIN, Hp-spaces of several variables, Acta Math., 129 (1972), 137-193. Zbl0257.46078MR56 #6263
  3. [3] S. JANSON, Characterizations of H1 by singular integral transforms on martingales and Rn, Math. Scand., 41 (1977), 140-152. Zbl0369.42005MR57 #3729
  4. [4] S. JANSON, Mean oscillation and commutators of singular integral operators, Ark. Mat., 16 (1978), 263-270. Zbl0404.42013MR80j:42034
  5. [5] A. UCHIYAMA, Compactness of operators of Hankel type, Tôhoku Math. J., 30 (1978), 163-171. Zbl0384.47023MR57 #7243

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