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Mellin pseudodifferential operators techniques in the theory of singular integral operators on some Carleson curves

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Differential and Integral Operators

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 102))

Abstract

We consider an algebra A p (Γ,ω) of singular integral operators with slowly oscillating bounded coefficients acting in L p (Γ,ω), 1 < p < ∞, where Γ is a composed Carleson curve with logarithmic whirl points and ω is a power weight. The local analysis of operators A ∈ A p (Γ,ω) at singular points of the contours is based on the Mellin pseudodifferential operators method. This method gives effective formulas for the local symbols. These formulas describe the influence on the local symbol of both the curve and the weight in an explicit form.

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Authors and Affiliations

  1. Dept. of Mathematics Mechanics, Rostov State University, 5 ul. Zorge, Rostov-na-Donu, 344104, Russia

    V. S. Rabinovich

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  1. V. S. Rabinovich
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Editors and Affiliations

  1. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, 69978, Israel

    I. Gohberg

  2. NWFI-Mathematik, Universität Regensburg, D-93040, Regensburg, Germany

    R. Mennicken  & C. Tretter  & 

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Rabinovich, V.S. (1998). Mellin pseudodifferential operators techniques in the theory of singular integral operators on some Carleson curves. In: Gohberg, I., Mennicken, R., Tretter, C. (eds) Differential and Integral Operators. Operator Theory: Advances and Applications, vol 102. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8789-2_15

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  • DOI: https://doi.org/10.1007/978-3-0348-8789-2_15

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9774-7

  • Online ISBN: 978-3-0348-8789-2

  • eBook Packages: Springer Book Archive

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