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Boundedness of Some Convolution and Twisted Convolution Operators

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Singular Integral Operators, Factorization and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 142))

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Abstract

We considerL p —L q boundedness problems for some special integral operators with oscillations both in the symbols and in the kernels.Such kernels have singularities on the unit sphereS n-1and at infinity and are smooth on ℝn \ S n−1.The main purpose is to show how these features affect the boundedness picture.Some further problems are discussed.

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, University of Arkansas Fayetteville, AR, 72701, USA

    Alexey N. Karapetyants

  2. Departamento de Matemáticas, CINVESTAV del I.P.N.A. P. 14-740, 07000, México

    Enrique Ramírez de Arellano

Authors
  1. Alexey N. Karapetyants
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  2. Enrique Ramírez de Arellano
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Editor information

Editors and Affiliations

  1. Faculty of Mathematics, Technical University Chemnitz, Chemnitz, 09107, Germany

    Albrecht Böttcher

  2. Department of Mathematics and Computer Science, Vrije Universiteit Amsterdam, De Boelelaan, Amsterdam, NL-1081 HV, The Netherlands

    Marinus A. Kaashoek

  3. Departamento de Matemática, Instituto Superior Técnico, Ave. Rovisco Pais, Lisboa, 1049-001, Portugal

    Amarino Brites Lebre , António Ferreira dos Santos  & Frank-Olme Speck ,  & 

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© 2003 Springer Basel AG

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Karapetyants, A.N., de Arellano, E.R. (2003). Boundedness of Some Convolution and Twisted Convolution Operators. In: Böttcher, A., Kaashoek, M.A., Lebre, A.B., dos Santos, A.F., Speck, FO. (eds) Singular Integral Operators, Factorization and Applications. Operator Theory: Advances and Applications, vol 142. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8007-7_8

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  • DOI: https://doi.org/10.1007/978-3-0348-8007-7_8

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9401-2

  • Online ISBN: 978-3-0348-8007-7

  • eBook Packages: Springer Book Archive

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