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Pseudodifferential Operators in Function Spaces with Exponential Weights
Author(s) -
Schott Thomas
Publication year - 1999
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.19992000106
Subject(s) - mathematics , exponential type , pure mathematics , exponential function , pseudodifferential operators , function space , lift (data mining) , euclidean space , function (biology) , type (biology) , space (punctuation) , euclidean geometry , class (philosophy) , mathematical analysis , geometry , ecology , linguistics , philosophy , evolutionary biology , artificial intelligence , biology , computer science , data mining
This paper is a continuation of [17]. We study weighted function spaces of type B a pq ( u ) and F a pq ( u ) on the Euclidean space ℝ n , where u is a weight function of at most exponential growth. In particular, u(x) = exp(±| x |) is an admissible weight. We consider symbols which belong to the Hörmander class S u 1,δ , where u ∈ ℝ and 0 ≤ δ ≤ 1. We give sufficient conditions for the boundedness of the corresponding pseudodifferential operators in the above function spaces. As a main tool, we use molecular decompositions of these spaces. Furthermore, we prove that the spaces B a pq ( u ) and F a pq ( u ) have the lift property.