Geodesic
Theorems of Hardy--Littlewood type for signed measures on a~cone
Sbornik. Mathematics, Tome 186 (1995) no. 5, pp. 675-693

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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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     author = {Yu. N. Drozhzhinov and B. I. Zavialov},
     title = {Theorems of {Hardy--Littlewood} type for signed measures on a~cone},
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     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_5_a2/}
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Yu. N. Drozhzhinov; B. I. Zavialov. Theorems of Hardy--Littlewood type for signed measures on a~cone. Sbornik. Mathematics, Tome 186 (1995) no. 5, pp. 675-693. http://geodesic.mathdoc.fr/item/SM_1995_186_5_a2/