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The boundedness and the fredholm property of integral operators with anisotropically homogeneous kernels of compact type and variable coefficients

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Abstract

In the space L p (ℝn), 1 < p < ∞, we study a new wide class of integral operators with anisotropically homogeneous kernels. We obtain sufficient conditions for the boundedness of operators from this class. We consider the Banach algebra generated by operators with anisotropically homogeneous kernels of compact type and multiplicatively slowly oscillating coefficients. We establish a relationship between this algebra and multidimensional convolution operators, and construct a symbolic calculus for it. We also obtain necessary and sufficient conditions for the Fredholm property of operators from this algebra.

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Authors and Affiliations

  1. Southern Federal University, ul. B. Sadovaya 105, Rostov-on-Don, 344006, Russia

    V. M. Deundyak & E. I. Miroshnikova

Authors
  1. V. M. Deundyak
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  2. E. I. Miroshnikova
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Correspondence to V. M. Deundyak.

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Original Russian Text © V.M. Deundyak and E.I. Miroshnikova, 2012, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, No. 7, pp. 3–17.

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Deundyak, V.M., Miroshnikova, E.I. The boundedness and the fredholm property of integral operators with anisotropically homogeneous kernels of compact type and variable coefficients. Russ Math. 56, 1–14 (2012). https://doi.org/10.3103/S1066369X12070018

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