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R. Beals (1975)
A general calculus of pseudodifferential operatorsDuke Mathematical Journal, 42
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Abstract. The paper is concerned with function spaces of Sobolev type and of Besov type of variable order of differentiation. The definition and the study of these spaces is closely connected with an appropriate class of pseudodifferential operators. 1980 Mathematics Subject Classification (1985 Revision): 46E35, 47G05; 35S99. The paper deals with function spaces of variable order of differentiation on the Euclidean w-space IRn. The definition of these spaces is closely connected with an appropriate class of pseudodifferential operators. In 1965-75 several papers had been published which relate function spaces and classes of pseudodifferential operators, see for example Unterberger and Bokobza [20], [21], ViSik and Eskin [22], [23]. Volevi and Kagan [24], Unterberger [19], Kumano-go and Tsutsumi [8], Beals [1]. Later on, in 1981, Beals [2] considered weighted distribution spaces based on the very general Weyl calculus of pseudodifferential operators. But all the function spaces defined and studied in these papers are spaces of Sobolev type or Besselpotential type. In contrast to this, we defined in [10] and [11] function spaces of Besov type of variable order of differentiation. Their definition is based on decompositions of R" x IR% which are induced by Symbols a(x, ) of appropriate pseudodifferential
Forum Mathematicum – de Gruyter
Published: Jan 1, 1991
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