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Mat. Sb., 1995, Volume 186, Number 5, Pages 49–68 (Mi msb36)  

This article is cited in 4 scientific papers (total in 4 papers)

Theorems of Hardy–Littlewood type for signed measures on a cone

Yu. N. Drozhzhinov, B. I. Zavialov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: It is known that the positivity condition plays an important role in theorems of Hardy–Littlewood type. In the multi-dimensional case this condition can be relaxed significantly by replacing it with the condition of sign-definiteness on trajectories along which asymptotic properties are investigated. A number of theorems are proved in this paper that demonstrate this effect. Our main tool is a theorem on division of tempered distributions by a homogeneous polynomial, preserving the corresponding quasi-asymptotics. The results obtained are used to study the asymptotic behaviour at a boundary point of holomorphic functions in tubular domains over cones.

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English version:
Sbornik: Mathematics, 1995, 186:5, 675–693

Bibliographic databases:

UDC: 517.53
MSC: Primary 32A40, 40E05; Secondary 46F12
Received: 15.09.1994

Citation: Yu. N. Drozhzhinov, B. I. Zavialov, “Theorems of Hardy–Littlewood type for signed measures on a cone”, Mat. Sb., 186:5 (1995), 49–68; Sb. Math., 186:5 (1995), 675–693

Citation in format AMSBIB
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\by Yu.~N.~Drozhzhinov, B.~I.~Zavialov
\paper Theorems of Hardy--Littlewood type for signed measures on a~cone
\jour Mat. Sb.
\yr 1995
\vol 186
\issue 5
\pages 49--68
\mathnet{http://mi.mathnet.ru/msb36}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1341084}
\zmath{https://zbmath.org/?q=an:0842.40002}
\transl
\jour Sb. Math.
\yr 1995
\vol 186
\issue 5
\pages 675--693
\crossref{https://doi.org/10.1070/SM1995v186n05ABEH000036}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995TC19700003}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. N. Drozhzhinov, B. I. Zavialov, “Local Tauberian theorems in spaces of distributions related to cones, and their applications”, Izv. Math., 61:6 (1997), 1171–1214  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Yu. N. Drozhzhinov, B. I. Zavialov, “Asymptotically homogeneous generalized functions and boundary properties of functions holomorphic in tubular cones”, Izv. Math., 70:6 (2006), 1117–1164  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Estrada R., Vindas J., “On Tauber's Second Tauberian Theorem”, Tohoku Math. J., 64:4 (2012), 539–560  crossref  mathscinet  zmath  isi
    4. Yu. N. Drozhzhinov, “Multidimensional Tauberian theorems for generalized functions”, Russian Math. Surveys, 71:6 (2016), 1081–1134  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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