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.
\Bibitem{DroZav95}
\by Yu.~N.~Drozhzhinov, B.~I.~Zavialov
\paper Theorems of Hardy--Littlewood type for signed measures on a~cone
\jour Sb. Math.
\yr 1995
\vol 186
\issue 5
\pages 675--693
\mathnet{http://mi.mathnet.ru/eng/sm36}
\crossref{https://doi.org/10.1070/SM1995v186n05ABEH000036}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1341084}
\zmath{https://zbmath.org/?q=an:0842.40002}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995TC19700003}
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https://doi.org/10.1070/SM1995v186n05ABEH000036
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