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
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
MSC: Primary 32A40, 40E05; Secondary 46F12
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
\by Yu.~N.~Drozhzhinov, B.~I.~Zavialov
\paper Theorems of Hardy--Littlewood type for signed measures on a~cone
\jour Mat. Sb.
\jour Sb. Math.
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This publication is cited in the following articles:
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
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
Estrada R., Vindas J., “On Tauber's Second Tauberian Theorem”, Tohoku Math. J., 64:4 (2012), 539–560
Yu. N. Drozhzhinov, “Multidimensional Tauberian theorems for generalized functions”, Russian Math. Surveys, 71:6 (2016), 1081–1134
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