Russian Mathematical Surveys
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Russian Mathematical Surveys, 2013, Volume 68, Issue 6, Pages 973–1026
DOI: https://doi.org/10.1070/RM2013v068n06ABEH004868 (Mi rm9556) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Non-homogeneous harmonic analysis: 16 years of development

A. L. Volberga, V. Ya. Èidermanb

a Michigan State University, East Lansing, MI, USA
b University of Wisconsin-Madison, Madison, WI, USA
English version PDF (1015 kB) Citations (13)
References:
PDF
HTML
DOI: https://doi.org/10.1070/RM2013v068n06ABEH004868
Abstract: This survey contains results and methods in the theory of singular integrals, a theory which has been developing dramatically in the last 15–20 years. The central (although not the only) topic of the paper is the connection between the analytic properties of integrals and operators with Calderón–Zygmund kernels and the geometric properties of the measures. The history is traced of the classical Painlevé problem of describing removable singularities of bounded analytic functions, which has provided a strong incentive for the development of this branch of harmonic analysis. The progress of recent decades has largely been based on the creation of an apparatus for dealing with non-homogeneous measures, and much attention is devoted to this apparatus here. Several open questions are stated, first and foremost in the multidimensional case, where the method of curvature of a measure is not available.
Bibliography: 128 titles.
Keywords: analytic capacity, Vitushkin's conjecture, Calderón–Zygmund operators and capacities, $T(1)$- and $T(b)$-theorems, rectifiable sets and measures, singular integrals and operators.
Funding agency Grant number
National Science Foundation DMS-0758552
Received: 03.05.2013
Russian version:
Uspekhi Matematicheskikh Nauk, 2013, Volume 68, Issue 6(414), Pages 3–58
DOI: https://doi.org/10.4213/rm9556
Bibliographic databases:
Document Type: Article
UDC: 517.53+517.98
MSC: 30C85, 31C15, 42B20
Language: English
Original paper language: Russian
Citation: A. L. Volberg, V. Ya. Èiderman, “Non-homogeneous harmonic analysis: 16 years of development”, Uspekhi Mat. Nauk, 68:6(414) (2013), 3–58; Russian Math. Surveys, 68:6 (2013), 973–1026
Citation in format AMSBIB
\Bibitem{VolEid13}
\by A.~L.~Volberg, V.~Ya.~\`Eiderman
\paper Non-homogeneous harmonic analysis: 16~years of development
\jour Uspekhi Mat. Nauk
\yr 2013
\vol 68
\issue 6(414)
\pages 3--58
\mathnet{http://mi.mathnet.ru/rm9556}
\crossref{https://doi.org/10.4213/rm9556}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3203192}
\zmath{https://zbmath.org/?q=an:1293.30057}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2013RuMaS..68..973V}
\elib{https://elibrary.ru/item.asp?id=21277011}
\transl
\jour Russian Math. Surveys
\yr 2013
\vol 68
\issue 6
\pages 973--1026
\crossref{https://doi.org/10.1070/RM2013v068n06ABEH004868}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000332667100001}
\elib{https://elibrary.ru/item.asp?id=22096008}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899741180}
Linking options:
  • https://www.mathnet.ru/eng/rm9556
  • https://doi.org/10.1070/RM2013v068n06ABEH004868
  • https://www.mathnet.ru/eng/rm/v68/i6/p3
    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Успехи математических наук Russian Mathematical Surveys
    Statistics & downloads:
    Abstract page:1186
    Russian version PDF:329
    English version PDF:43
    References:103
    First page:70
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024