The Hilbert Transform of a Measure

Let $\fre$ be a homogeneous subset of $\bbR$ in the sense of Carleson. Let $\mu$ be a finite positive measure on $\bbR$ and $H_\mu(x)$ its Hilbert transform. We prove that if $\lim_{t\to\infty} t \abs{\fre\cap\{x\mid\abs{H_\mu(x)}>t\}}=0$, then $\mu_s(\fre)=0$, where $\mu_\s$ is the singular part...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Hauptverfasser:	Poltoratski, Alexei, Simon, Barry, Zinchenko, Maxim
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics - Mathematical Physics Physics - Mathematical Physics
Online-Zugang:	Volltext bestellen
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

container_end_page
container_issue
container_start_page
container_title
container_volume
creator	Poltoratski, Alexei Simon, Barry Zinchenko, Maxim
description	Let $\fre$ be a homogeneous subset of $\bbR$ in the sense of Carleson. Let $\mu$ be a finite positive measure on $\bbR$ and $H_\mu(x)$ its Hilbert transform. We prove that if $\lim_{t\to\infty} t \abs{\fre\cap\{x\mid\abs{H_\mu(x)}>t\}}=0$, then $\mu_s(\fre)=0$, where $\mu_\s$ is the singular part of $\mu$.
doi_str_mv	10.48550/arxiv.0811.0791
format	Article
fullrecord	<record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_0811_0791</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>0811_0791</sourcerecordid><originalsourceid>FETCH-LOGICAL-a651-23c89fd5a33e533d06c4bf80e9773608187df1cf846f93ed26a176433bd0e7623</originalsourceid><addsrcrecordid>eNotzjsLwjAUhuEsDqLuThLcW5Oe5tJRxBsoLt3LaXOCBWslVdF_73X6tvd7GBtLEadWKTHD8KjvsbBSxsJkss-m-ZH4pj6VFK48D3jufBsa3nqOfE_Y3QINWc_jqaPRfwcsXy3zxSbaHdbbxXwXoVYySqCymXcKAUgBOKGrtPRWUGYM6PejNc7LyttU-wzIJRql0SlA6QQZncCATX7Zr7G4hLrB8Cw-1uJjhRdMPjcO</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>The Hilbert Transform of a Measure</title><source>arXiv.org</source><creator>Poltoratski, Alexei ; Simon, Barry ; Zinchenko, Maxim</creator><creatorcontrib>Poltoratski, Alexei ; Simon, Barry ; Zinchenko, Maxim</creatorcontrib><description>Let $\fre$ be a homogeneous subset of $\bbR$ in the sense of Carleson. Let $\mu$ be a finite positive measure on $\bbR$ and $H_\mu(x)$ its Hilbert transform. We prove that if $\lim_{t\to\infty} t \abs{\fre\cap\{x\mid\abs{H_\mu(x)}>t\}}=0$, then $\mu_s(\fre)=0$, where $\mu_\s$ is the singular part of $\mu$.</description><identifier>DOI: 10.48550/arxiv.0811.0791</identifier><language>eng</language><subject>Mathematics - Mathematical Physics ; Physics - Mathematical Physics</subject><creationdate>2008-11</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/0811.0791$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.0811.0791$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Poltoratski, Alexei</creatorcontrib><creatorcontrib>Simon, Barry</creatorcontrib><creatorcontrib>Zinchenko, Maxim</creatorcontrib><title>The Hilbert Transform of a Measure</title><description>Let $\fre$ be a homogeneous subset of $\bbR$ in the sense of Carleson. Let $\mu$ be a finite positive measure on $\bbR$ and $H_\mu(x)$ its Hilbert transform. We prove that if $\lim_{t\to\infty} t \abs{\fre\cap\{x\mid\abs{H_\mu(x)}>t\}}=0$, then $\mu_s(\fre)=0$, where $\mu_\s$ is the singular part of $\mu$.</description><subject>Mathematics - Mathematical Physics</subject><subject>Physics - Mathematical Physics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzjsLwjAUhuEsDqLuThLcW5Oe5tJRxBsoLt3LaXOCBWslVdF_73X6tvd7GBtLEadWKTHD8KjvsbBSxsJkss-m-ZH4pj6VFK48D3jufBsa3nqOfE_Y3QINWc_jqaPRfwcsXy3zxSbaHdbbxXwXoVYySqCymXcKAUgBOKGrtPRWUGYM6PejNc7LyttU-wzIJRql0SlA6QQZncCATX7Zr7G4hLrB8Cw-1uJjhRdMPjcO</recordid><startdate>20081105</startdate><enddate>20081105</enddate><creator>Poltoratski, Alexei</creator><creator>Simon, Barry</creator><creator>Zinchenko, Maxim</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20081105</creationdate><title>The Hilbert Transform of a Measure</title><author>Poltoratski, Alexei ; Simon, Barry ; Zinchenko, Maxim</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a651-23c89fd5a33e533d06c4bf80e9773608187df1cf846f93ed26a176433bd0e7623</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Mathematics - Mathematical Physics</topic><topic>Physics - Mathematical Physics</topic><toplevel>online_resources</toplevel><creatorcontrib>Poltoratski, Alexei</creatorcontrib><creatorcontrib>Simon, Barry</creatorcontrib><creatorcontrib>Zinchenko, Maxim</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Poltoratski, Alexei</au><au>Simon, Barry</au><au>Zinchenko, Maxim</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Hilbert Transform of a Measure</atitle><date>2008-11-05</date><risdate>2008</risdate><abstract>Let $\fre$ be a homogeneous subset of $\bbR$ in the sense of Carleson. Let $\mu$ be a finite positive measure on $\bbR$ and $H_\mu(x)$ its Hilbert transform. We prove that if $\lim_{t\to\infty} t \abs{\fre\cap\{x\mid\abs{H_\mu(x)}>t\}}=0$, then $\mu_s(\fre)=0$, where $\mu_\s$ is the singular part of $\mu$.</abstract><doi>10.48550/arxiv.0811.0791</doi><oa>free_for_read</oa></addata></record>
fulltext	fulltext_linktorsrc
identifier	DOI: 10.48550/arxiv.0811.0791
ispartof
issn
language	eng
recordid	cdi_arxiv_primary_0811_0791
source	arXiv.org
subjects	Mathematics - Mathematical Physics Physics - Mathematical Physics
title	The Hilbert Transform of a Measure
url	https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-03T12%3A08%3A06IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20Hilbert%20Transform%20of%20a%20Measure&rft.au=Poltoratski,%20Alexei&rft.date=2008-11-05&rft_id=info:doi/10.48550/arxiv.0811.0791&rft_dat=%3Carxiv_GOX%3E0811_0791%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true