ON THE lp-NORM OF THE DISCRETE HILBERT TRANSFORM

被引：6

作者：

Banuelos, Rodrigo ^{[1
]}

Kwasnicki, Mateusz ^{[2
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Wroclaw Univ Sci & Technol, Fac Pure & Appl Math, Wroclaw, Poland

来源：

DUKE MATHEMATICAL JOURNAL | 2019年 / 168卷 / 03期

基金：

美国国家科学基金会;

关键词：

HARMONIC-ANALYSIS; RIESZ TRANSFORMS; SHARP INEQUALITIES; MARTINGALE TRANSFORMS; CONJUGATE FUNCTION; ANALOGS; OPERATORS; PROOF;

D O I：

10.1215/00127094-2018-0047

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using a representation of the discrete Hilbert transform in terms of martingales arising from Doob h-processes, we prove that its l(p) -norm, 1 < p < infinity, is bounded above by the L-p-norm of the continuous Hilbert transform. Together with the already known lower bound, this resolves the long-standing conjecture that the norms of these operators are equal.

引用

页码：471 / 504

页数：34

共 50 条

[1] AN LP-NORM INEQUALITY
WU, PY
[J]. AMERICAN MATHEMATICAL MONTHLY, 1983, 90 (06): : 411 - 412
[2] LP-NORM DECONVOLUTION
DEBEYE, HWJ
VANRIEL, P
[J]. GEOPHYSICAL PROSPECTING, 1990, 38 (04) : 381 - 403
[3] Discrete total lp-norm approximation problem for the exponential function
Jukic, D
Marosevic, T
Scitovski, R
[J]. APPLIED MATHEMATICS AND COMPUTATION, 1998, 94 (2-3) : 137 - 143
[4] Trigonometric approximation in Lp-norm
Leindler, L
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 302 (01) : 129 - 136
[5] On the Simultaneous Approximation in Lp-norm
周颂平
[J]. Journal of Mathematical Research with Applications, 1984, (04) : 36 - 36
[6] lp-Norm Multiway Cut
Chandrasekaran, Karthekeyan
Wang, Weihang
[J]. ALGORITHMICA, 2022, 84 (09) : 2667 - 2701
[7] Lp-norm spherical copulas
Bernard, Carole
Mueller, Alfred
Oesting, Marco
[J]. JOURNAL OF MULTIVARIATE ANALYSIS, 2024, 201
[8] Oblivious Routing for the Lp-norm
Englert, Matthias
Raecke, Harald
[J]. 2009 50TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE: FOCS 2009, PROCEEDINGS, 2009, : 32 - 40
[9] Trigonometric approximation of functions in Lp-norm
Chandra, P
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 275 (01) : 13 - 26
[10] Lp-NORM ESTIMATE FOR THE BERGMAN PROJECTIONS
Zhang, Shuo
[J]. HOUSTON JOURNAL OF MATHEMATICS, 2020, 46 (03): : 771 - 796

← 1 2 3 4 5 →