A generalization of Miyachi's theorem

Radouan Daher; Takeshi Kawazoe; Hatem Mejjaoli

doi:10.2969/jmsj/06120551

A generalization of Miyachi's theorem

Radouan Daher, Takeshi Kawazoe, Hatem Mejjaoli

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

9 Citations (Scopus)

Abstract

The classical Hardy theorem on R, which asserts f and the Fourier transform of / cannot both be very small, was generalized by Miyachi in terms of L ¹ + L∞ and log⁺-functions. In this paper we generalize Miyachi's theorem for R^d and then for other generalized Fourier transforms such as the Chébli-Trimèche and the Dunkl transforms.

Original language	English
Pages (from-to)	551-558
Number of pages	8
Journal	Journal of the Mathematical Society of Japan
Volume	61
Issue number	2
DOIs	https://doi.org/10.2969/jmsj/06120551
Publication status	Published - 2009 Apr
Externally published	Yes

Keywords

Chebli-Trimèche transform
Dunkl transform
Hardy's theorem
Miyachi's theorem
Radon transform

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.2969/jmsj/06120551

Cite this

@article{21e56aa36b56458b92d475d4d53f999c,

title = "A generalization of Miyachi's theorem",

abstract = "The classical Hardy theorem on R, which asserts f and the Fourier transform of / cannot both be very small, was generalized by Miyachi in terms of L 1 + L∞ and log+-functions. In this paper we generalize Miyachi's theorem for Rd and then for other generalized Fourier transforms such as the Ch{\'e}bli-Trim{\`e}che and the Dunkl transforms.",

keywords = "Chebli-Trim{\`e}che transform, Dunkl transform, Hardy's theorem, Miyachi's theorem, Radon transform",

author = "Radouan Daher and Takeshi Kawazoe and Hatem Mejjaoli",

year = "2009",

month = apr,

doi = "10.2969/jmsj/06120551",

language = "English",

volume = "61",

pages = "551--558",

journal = "Journal of the Mathematical Society of Japan",

issn = "0025-5645",

publisher = "Mathematical Society of Japan - Kobe University",

number = "2",

}

TY - JOUR

T1 - A generalization of Miyachi's theorem

AU - Daher, Radouan

AU - Kawazoe, Takeshi

AU - Mejjaoli, Hatem

PY - 2009/4

Y1 - 2009/4

N2 - The classical Hardy theorem on R, which asserts f and the Fourier transform of / cannot both be very small, was generalized by Miyachi in terms of L 1 + L∞ and log+-functions. In this paper we generalize Miyachi's theorem for Rd and then for other generalized Fourier transforms such as the Chébli-Trimèche and the Dunkl transforms.

AB - The classical Hardy theorem on R, which asserts f and the Fourier transform of / cannot both be very small, was generalized by Miyachi in terms of L 1 + L∞ and log+-functions. In this paper we generalize Miyachi's theorem for Rd and then for other generalized Fourier transforms such as the Chébli-Trimèche and the Dunkl transforms.

KW - Chebli-Trimèche transform

KW - Dunkl transform

KW - Hardy's theorem

KW - Miyachi's theorem

KW - Radon transform

UR - http://www.scopus.com/inward/record.url?scp=67650976693&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67650976693&partnerID=8YFLogxK

U2 - 10.2969/jmsj/06120551

DO - 10.2969/jmsj/06120551

M3 - Article

AN - SCOPUS:67650976693

SN - 0025-5645

VL - 61

SP - 551

EP - 558

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

IS - 2

ER -

A generalization of Miyachi's theorem

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this