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On Function Spaces of Variable Order of Differentiation

On Function Spaces of Variable Order of Differentiation 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

On Function Spaces of Variable Order of Differentiation

Forum Mathematicum , Volume 3 (3) – Jan 1, 1991

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References (22)

Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/form.1991.3.1
Publisher site
See Article on Publisher Site

Abstract

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

Journal

Forum Mathematicumde Gruyter

Published: Jan 1, 1991

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