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Function Spaces with Exponential Weights I
Author(s) -
Schott Thomas
Publication year - 1998
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19981890115
Subject(s) - mathematics , exponential type , exponential function , weight function , completeness (order theory) , euclidean space , euclidean geometry , pure mathematics , exponential growth , function (biology) , entire function , type (biology) , space (punctuation) , function space , mathematical analysis , geometry , ecology , evolutionary biology , linguistics , philosophy , biology
In this paper we define weighted function spaces of type B s pq ( u ) and F s pq ( u ) on the Euclidean space IR n , where u is a weight function of at most exponential growth. In particular, u ( x ) = exp(±|χ|) is an admissible weight. We prove some basic properties of these spaces, such as completeness and density of the smooth functions.