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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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Sbornik: Mathematics, 1995, 186:5, 675–693
Bibliographic databases:
Document Type:
Article
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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\pages 49--68
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\jour Sb. Math.
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\issue 5
\pages 675--693
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http://mi.mathnet.ru/eng/msb36 http://mi.mathnet.ru/eng/msb/v186/i5/p49
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This publication is cited in the following articles:
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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
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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
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Estrada R., Vindas J., “On Tauber's Second Tauberian Theorem”, Tohoku Math. J., 64:4 (2012), 539–560
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Yu. N. Drozhzhinov, “Multidimensional Tauberian theorems for generalized functions”, Russian Math. Surveys, 71:6 (2016), 1081–1134
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