• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文学位 >Multiplier theorems, square function estimates, and Bochner-Riesz means associated with rough domains.
【24h】

Multiplier theorems, square function estimates, and Bochner-Riesz means associated with rough domains.

机译：乘子定理，平方函数估计和Bochner-Riesz均值与粗糙域相关。

获取原文
获取原文并翻译 | 示例
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

This thesis contains results of the author from [12], [13], [14], and [15]. In the first part of the thesis, we will prove a characterization of restricted strong type (p; p) boundedness of multiplier operators whose multiplier is a radial function on R3 supported compactly away from the origin, in the range 1 < p < 13/12. This result complements a result of Heo, Nazarov, and Seeger, who obtained a characterization of radial Fourier multiplier operators bounded on Lp(Rd) in dimensions d > 4 for the range 1 < p < (2d--2)/(d+1).;In the second part of the thesis, we introduce and define Bochner-Riesz multipliers associated with convex planar domains. Such multipliers were first studied by Seeger and Ziesler, and we discuss their results as background. We then discuss new results addressing the question of sharpness of Seeger and Ziesler's theorem. We introduce the additive combinatorial notion of "additive energy" of the boundary of a convex domain which we will show gives a sufficient criteria for obtaining improved Lp bounds for Bochner-Riesz multipliers.;In the third part of the thesis, we will introduce general Fourier multipliers associated with convex planar domains and prove a criterion for Lp boundedness of the corresponding multiplier operators. The methods used to obtain multiplier theorems in this section will involve analysis of "half-wave" operators associated with convex domains.;In the fourth part of the thesis, we will discuss a related square function result and obtain new multiplier theorems as a corollary, which we will interpolate with our results from the third part of the thesis to obtain our most general quasiradial multiplier theorem.
机译：本文包含作者[12]，[13]，[14]和[15]的结果。在本文的第一部分中，我们将证明乘法器算子的受限强类型（p; p）有界性的刻画，其乘子是R3上的径向函数，紧密地远离原点，范围1 <13 / 12此结果补充了Heo，Nazarov和Seeger的结果，他们获得了在范围p <（2d--2）/（d + 1）.;在论文的第二部分，我们介绍并定义了与凸平面域相关的Bochner-Riesz乘数。这种乘数最初是由Seeger和Ziesler研究的，我们将其结果作为背景进行讨论。然后，我们讨论解决Seeger和Ziesler定理的敏锐度问题的新结果。我们介绍了凸域边界的“加和能量”的加和组合概念，我们将证明它为获得Bochner-Riesz乘子的Lp界提供了充分的标准。在论文的第三部分，我们将介绍一般的与凸平面域相关联的傅立叶乘法器，并证明了相应乘法器算子的Lp有界性的准则。本节中用于获得乘法定理的方法将涉及分析与凸域相关的“半波”算符。在本文的第四部分，我们将讨论相关的平方函数结果，并得出新的乘法定理作为推论，我们将在论文第三部分中对我们的结果进行插值，以获得最通用的拟辐射系数定理。

著录项

  • 作者

    Cladek, Laura.;

  • 作者单位

    The University of Wisconsin - Madison.;

  • 授予单位 The University of Wisconsin - Madison.;
  • 学科 Mathematics.
  • 学位 Ph.D.
  • 年度 2016
  • 页码 187 p.
  • 总页数 187
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号