Weighted estimates for the discrete hilbert transform

E. Liflyand

doi:10.1007/978-3-319-27466-9_5

Weighted estimates for the discrete hilbert transform

E. Liflyand

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

7 Scopus citations

Abstract

The Paley-Wiener theorem states that the Hilbert transform of an integrable odd function, which is monotone on ℝ₊, is integrable. In this paper we prove weighted analogs of this theorem for sequences and their discrete Hilbert transforms under the assumption of general monotonicity for an even/odd sequence.

Original language	English
Title of host publication	Applied and Numerical Harmonic Analysis
Publisher	Springer International Publishing
Pages	59-69
Number of pages	11
Edition	9783319274652
DOIs	https://doi.org/10.1007/978-3-319-27466-9_5
State	Published - 2016

Publication series

Name	Applied and Numerical Harmonic Analysis
Number	9783319274652
ISSN (Print)	2296-5009
ISSN (Electronic)	2296-5017

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2016.

Keywords

Discrete hilbert transform
General monotone functions and sequences
Hilbert transform
Weighted integrability

Access to Document

10.1007/978-3-319-27466-9_5

Cite this

@inbook{53ae62ac8c734bb2a13cd38bbd2d75a3,

title = "Weighted estimates for the discrete hilbert transform",

abstract = "The Paley-Wiener theorem states that the Hilbert transform of an integrable odd function, which is monotone on ℝ+, is integrable. In this paper we prove weighted analogs of this theorem for sequences and their discrete Hilbert transforms under the assumption of general monotonicity for an even/odd sequence.",

keywords = "Discrete hilbert transform, General monotone functions and sequences, Hilbert transform, Weighted integrability",

author = "E. Liflyand",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.",

year = "2016",

doi = "10.1007/978-3-319-27466-9_5",

language = "אנגלית",

series = "Applied and Numerical Harmonic Analysis",

publisher = "Springer International Publishing",

number = "9783319274652",

pages = "59--69",

booktitle = "Applied and Numerical Harmonic Analysis",

edition = "9783319274652",

}

TY - CHAP

T1 - Weighted estimates for the discrete hilbert transform

AU - Liflyand, E.

N1 - Publisher Copyright: © Springer International Publishing Switzerland 2016.

PY - 2016

Y1 - 2016

N2 - The Paley-Wiener theorem states that the Hilbert transform of an integrable odd function, which is monotone on ℝ+, is integrable. In this paper we prove weighted analogs of this theorem for sequences and their discrete Hilbert transforms under the assumption of general monotonicity for an even/odd sequence.

AB - The Paley-Wiener theorem states that the Hilbert transform of an integrable odd function, which is monotone on ℝ+, is integrable. In this paper we prove weighted analogs of this theorem for sequences and their discrete Hilbert transforms under the assumption of general monotonicity for an even/odd sequence.

KW - Discrete hilbert transform

KW - General monotone functions and sequences

KW - Hilbert transform

KW - Weighted integrability

UR - http://www.scopus.com/inward/record.url?scp=85047292744&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-27466-9_5

DO - 10.1007/978-3-319-27466-9_5

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.chapter???

AN - SCOPUS:85047292744

T3 - Applied and Numerical Harmonic Analysis

SP - 59

EP - 69

BT - Applied and Numerical Harmonic Analysis

PB - Springer International Publishing

ER -

Weighted estimates for the discrete hilbert transform

Abstract

Publication series

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this