Sharp bounds for multiplier operators of negative indices associated with degenerate curves

被引：0
作者：
Sanghyuk Lee
Ihyeok Seo
机构：
[1] Seoul National University,School of Mathematical Sciences
来源：
Mathematische Zeitschrift | 2011年 / 267卷
关键词：
Multiplier; Negative index; Primary 42B15; 42B25;
D O I：
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摘要：
In this note we show the sharp Lp–Lq boundedness of multiplier operators of Bochner–Riesz type having negative indices of which singularity is located in degenerate curve in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^2}$$\end{document} . Lp–Lq boundedness of their maximal operators is also obtained.
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页码：291 / 323
页数：32
相关论文
共 33 条
[1]  
Bak J.-G.(1997)Sharp estimates for the Bochner-Riesz operator of negative order in Proc. Am. Math. Soc. 125 1977-1986
[2]  
Börjeson L.(1986)Estimates for the Bochner-Riesz operator with negative index Indiana U. Math. J. 35 225-233
[3]  
Carbery A.(1983)The boundedness of the maximal Bochner-Riesz operator on Duke Math. J. 50 409-416
[4]  
Carbery A.(2000)Weighted inequalities for Bochner-Riesz means in the plane Q. J. Math. 51 155-167
[5]  
Seeger A.(1988)Almost-everywhere convergence of Fourier integrals for functions in Sobolev spaces, and an Rev. Mat. Iberoamericana 4 319-337
[6]  
Carbery A.(1972)-localisation principle Studia Math. 44 287-299
[7]  
Soria F.(2005)Oscillatory integrals and a multiplier problem for the disc J. Funct. Anal. 218 150-167
[8]  
Carleson L.(1985)Sharp Proc. Am. Math. Soc. 95 16-20
[9]  
Sjolin P.(1985)- Trans. Amer. Math. Soc. 287 223-238
[10]  
Cho Y.(1979) estimates for Bochner–Riesz operators of negative index in Duke Math. J. 46 505-511
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