Weighted estimates for conic Fourier multipliers

被引：0
作者：
Antonio Córdoba
Keith M. Rogers
机构：
[1] Universidad Autónoma de Madrid,Departamento de Matemáticas and Instituto de Ciencias Matemáticas CSIC
[2] Consejo Superior de Investigaciones Científicas,UAM
来源：
Mathematische Zeitschrift | 2014年 / 278卷
关键词：
Fourier multipliers; Maximal operators; Lacunary directions; Primary 42B25; Secondary 26B05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We prove a weighted inequality which controls conic Fourier multiplier operators in terms of lacunary directional maximal operators. By bounding the maximal operators, this enables us to conclude that the multiplier operators are bounded on Lp(R3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p(\mathbb {R}^3)$$\end{document} with 1<p<∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1<p<\infty $$\end{document}.
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页码：431 / 440
页数：9
相关论文
共 41 条
  • [1] Alfonseca A(2003)Strong type inequalities and an almost-orthogonality principle for families of maximal operators along directions in J. Lond. Math. Soc. 67 208-218
  • [2] Alfonseca A(2003)A remark on maximal operators along directions in Math. Res. Lett. 10 41-49
  • [3] Soria F(2009)Kakeya sets and directional maximal operators in the plane Duke Math. J. 147 55-77
  • [4] Vargas A(2006)A Stein conjecture for the circle Math. Ann. 336 671-695
  • [5] Bateman M(2012)Weighted norm inequalities for oscillatory integrals with finite type phases on the line Adv. Math. 229 2159-2183
  • [6] Bennett J(1985)A weighted inequality for the maximal Bochner–Riesz operator on Trans. Am. Math. Soc. 287 673-680
  • [7] Carbery A(1988)Differentiation in lacunary directions and an extension of the Marcinkiewicz multiplier theorem Ann. Inst. Fourier 38 157-169
  • [8] Soria F(2000)Weighted inequalities for Bochner–Riesz means in the plane Q. J. Math. 51 155-167
  • [9] Vargas A(1985)On almost everywhere convergence of Bochner–Riesz means in higher dimensions Proc. Am. Math. Soc. 95 16-20
  • [10] Bennett J(1974)Weighted norm inequalities for maximal functions and singular integrals Studia Math. 51 241-250
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