The weak-type (1, 1) of Fourier integral operators of order -(n - 1)/2

Terence Tao

doi:10.1017/s1446788700008661

The weak-type (1, 1) of Fourier integral operators of order -(n - 1)/2

Terence Tao^*

^*Corresponding author for this work

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

33 Citations (Scopus)

Abstract

Let T be a Fourier integral operator on ℝⁿ of order -(n - 1)/2. Seeger, Sogge, and Stein showed (among other things) that T maps the Hardy space H¹ to L¹. In this note we show that T is also of weak-type (1, 1). The main ideas are a decomposition of T into non-degenerate and degenerate components, and a factorization of the non-degenerate portion.

Original language	English
Pages (from-to)	1-21
Number of pages	21
Journal	Journal of the Australian Mathematical Society
Volume	76
Issue number	1
DOIs	https://doi.org/10.1017/s1446788700008661
Publication status	Published - Feb 2004
Externally published	Yes

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abstract = "Let T be a Fourier integral operator on ℝn of order -(n - 1)/2. Seeger, Sogge, and Stein showed (among other things) that T maps the Hardy space H1 to L1. In this note we show that T is also of weak-type (1, 1). The main ideas are a decomposition of T into non-degenerate and degenerate components, and a factorization of the non-degenerate portion.",

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AB - Let T be a Fourier integral operator on ℝn of order -(n - 1)/2. Seeger, Sogge, and Stein showed (among other things) that T maps the Hardy space H1 to L1. In this note we show that T is also of weak-type (1, 1). The main ideas are a decomposition of T into non-degenerate and degenerate components, and a factorization of the non-degenerate portion.

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The weak-type (1, 1) of Fourier integral operators of order -(n - 1)/2

Abstract

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