Characterizations of bounded mean oscillation on the polydisk in terms of Hankel operators and Carleson measures

Ferguson, Sarah Hargus; Sadosky, Cora

doi:10.1007/bf02788991

Cited by 61 publications

(53 citation statements)

References 22 publications

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“…See [4]. Therefore, for a small constant c to be chosen below, we can assume that II b[[ BMO(rec)<~ ~, for otherwise we have a lower bound on B2--,2.…”

Section: Rcumentioning

confidence: 98%

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A characterization of product BMO by commutators

2002

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“…See [4]. Therefore, for a small constant c to be chosen below, we can assume that II b[[ BMO(rec)<~ ~, for otherwise we have a lower bound on B2--,2.…”

Section: Rcumentioning

confidence: 98%

“…The second is a variant of Journ6's lemma, [61, (whose proof is included in the appendix). The third idea is that we have the estimates, the second of which was shown in [4], JJbllesMO(r,,,,) <~ cJJ[[Mb, a~], H2IIIL~-*L~ ~< e'lJbJJz~MO.…”

Section: Theorem 12 There Is a Constant C>0 Such That Iibiibmomentioning

confidence: 99%

A characterization of product BMO by commutators

2002

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“…We prove that a sufficient condition for these commutators to be bounded is given by our notion of logarithmic oscillation adapted to R N . This last interest is in the scope of the works [5,6,14] which can be seen as a motivation for this paper.…”

Section: Introductionmentioning

confidence: 99%

Logarithmic Mean Oscillation on the Polydisc, Multi-Parameter Paraproducts and Iterated Commutators

Sehba

2014

J Fourier Anal Appl

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Abstract. We introduce another notion of bounded logarithmic mean oscillation in the N -torus and give an equivalent definition in terms of boundedness of multi-parameter paraproducts from the dyadic little BMO, bmo d (T N ) to the dyadic product BMO space, BMO d (T N ). We also obtain a sufficient condition for the boundedness of the iterated commutators from the subspace of bmo(R N ) consisting of functions with support in [0,1] N to BMO(R N ).

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“…Proof of Theorem 1.3. The space bmo(T N ) has the following equivalent definitions ( [2,3]) that we need here.…”

Section: Comparison Via Multiplier Algebrasmentioning

confidence: 99%

An embedding relation for bounded mean oscillation on rectangles

Sehba

2014

Ann. Polon. Math.

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Abstract. In the two-parameter setting, we say a function belongs to the mean little BMO, if its mean over any interval and with respect to any of the two variables has uniformly bounded mean oscillation. This space has been recently introduced by S. Pott and the author in relation with the multiplier algebra of the product BMO of Chang-Fefferman. We prove that the Cotlar-Sadosky space of functions of bounded mean oscillation bmo(T N ) is a strict subspace of the mean little BMO.

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Characterizations of bounded mean oscillation on the polydisk in terms of Hankel operators and Carleson measures

Cited by 61 publications

References 22 publications

A characterization of product BMO by commutators

A characterization of product BMO by commutators

Logarithmic Mean Oscillation on the Polydisc, Multi-Parameter Paraproducts and Iterated Commutators

An embedding relation for bounded mean oscillation on rectangles

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