A local T(b) theorem for perfect multilinear Caldeŕon-Zygmund operators

Mariusz Mirek; Christoph Thiele

doi:10.1112/plms.12000

A local T(b) theorem for perfect multilinear Caldeŕon-Zygmund operators

Mariusz Mirek, Christoph Thiele

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We prove a multilinear local T(b) theorem that differs from previously considered multilinear local T(b) theorems in using exclusively general testing functions b as opposed to a mix of general testing functions and indicator functions. The main new feature is a set of relations between the various testing functions b that, to our knowledge has not been observed in the literature and is necessitated by our approach. For simplicity we restrict attention to the perfect dyadic model.

Original language	English (US)
Pages (from-to)	35-59
Number of pages	25
Journal	Proceedings of the London Mathematical Society
Volume	114
Issue number	1
DOIs	https://doi.org/10.1112/plms.12000
State	Published - 2017
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1112/plms.12000

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abstract = "We prove a multilinear local T(b) theorem that differs from previously considered multilinear local T(b) theorems in using exclusively general testing functions b as opposed to a mix of general testing functions and indicator functions. The main new feature is a set of relations between the various testing functions b that, to our knowledge has not been observed in the literature and is necessitated by our approach. For simplicity we restrict attention to the perfect dyadic model.",

author = "Mariusz Mirek and Christoph Thiele",

note = "Funding Information: M. Mirek was supported by the Hausdorff Center for Mathematics and NCN grant DEC-2012/05/D/ ST1/00053. C. Thiele was supported by the NSF grant DMS-1001535 and the Hausdorff Center for Mathematics. Publisher Copyright: {\textcopyright} 2017 London Mathematical Society.",

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N2 - We prove a multilinear local T(b) theorem that differs from previously considered multilinear local T(b) theorems in using exclusively general testing functions b as opposed to a mix of general testing functions and indicator functions. The main new feature is a set of relations between the various testing functions b that, to our knowledge has not been observed in the literature and is necessitated by our approach. For simplicity we restrict attention to the perfect dyadic model.

AB - We prove a multilinear local T(b) theorem that differs from previously considered multilinear local T(b) theorems in using exclusively general testing functions b as opposed to a mix of general testing functions and indicator functions. The main new feature is a set of relations between the various testing functions b that, to our knowledge has not been observed in the literature and is necessitated by our approach. For simplicity we restrict attention to the perfect dyadic model.

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A local T(b) theorem for perfect multilinear Caldeŕon-Zygmund operators

Abstract

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