Pointwise multipliers for functions of bounded mean oscillation

“…(2) A study of multipliers for BMO -spaces originated in 1976 by the paper of S. Janson [39] and developed by Y. Gotoh [22,23], E. Nakai and K. Yabuta [51,50]. TOME 57 (2007), FASCICULE 5 The previous discussion on the product distribution b × h can be summarized in the following lemma.…”

Section: Introduction and Overviewmentioning

confidence: 99%

On the Product of Functions in BMO and H^\text{1}

Bonami¹,

Iwaniec²,

Jones³

et al. 2007

Ann. inst. Fourier

108

124

View full text Add to dashboard Cite

“…Recall that BMO log (R n ) -the generalized BMO type space that has been introduced by Nakai and Yabuta [37] to characterize multipliers of BMO(R n )-is the space of all locally integrable functions f such that…”

Section: [B T ](F ) = Bt (F ) − T (Bf )mentioning

confidence: 99%

“…In the study of the pointwise multipliers for BMO(R n ), Nakai and Yabuta [37] introduced the space BMO log (R n ), consisting of locally integrable functions f with…”

Section: Some Preliminaries and Notationsmentioning

confidence: 99%

Bilinear decompositions and commutators of singular integral operators

2012

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract. Let b be a BM O-function. It is well-known that the linear commutator [b, T ] of a Calderón-Zygmund operator T does not, in general, map continuouslyIn this paper, we find the largest subspace H 1 b (R n ) such that all commutators of Calderón-Zygmund operators are continuous fromWe also study the commutators [b, T ] for T in a class K of sublinear operators containing almost all important operators in harmonic analysis. When T is linear, we prove that there exists a bilinear operators R = R T mapping continuouslywhere S is a bounded bilinear operator fromIn the particular case of T a Calderón-Zygmund operator satisfying T 1 = T * 1 = 0 and b in BM O log (R n )-the generalized BMO type space that has been introduced by Nakai and Yabuta to characterize multipliers of BMO(R n ) -we prove that the commutatorWhen T is sublinear, we prove that there exists a bounded subbilinear operator R = R T :The bilinear decomposition (1) and the subbilinear decomposition (2) allow us to give a general overview of all known weak and strong L 1 -estimates.

show abstract

Pointwise multipliers for functions of bounded mean oscillation

Abstract: Pointwise multipliers for functions of bounded mean oscillation By Eiichi NAKAI and K6z6 YABUTA*

Cited by 98 publications

References 3 publications

Pointwise Multipliers of Weighted BMO Spaces

Pointwise Multipliers of Weighted BMO Spaces

On the Product of Functions in BMO and H^\text{1}

Bilinear decompositions and commutators of singular integral operators

Contact Info

Product

Resources

About