The boundedness and the Fredholm property of integral operators with anisotropically homogeneous kernels of compact type and variable coefficients
type: Item
instance of: scholarly article
title: The boundedness and the Fredholm property of integral operators with anisotropically homogeneous kernels of compact type and variable coefficients
zbMATH Open document ID: 1269.47035
DOI: 10.3103/S1066369X12070018
author: V. M. Deundjak
author: E. I. Miroshnikova
published in: Russian Mathematics
publication date: 2012-11-20T00:00:00Z
review text: In the space \(L_p(\mathbb R^n), \, 1 < p < \infty\), a new class of integral operators with anisotropically homogeneous kernels is studied. Sufficient conditions are obtained for the boundedness of operators from this class. Further, the authors consider the Banach algebra generated by operators with anisotropically homogeneous kernels of compact type and multiplicative-slowly oscillating coefficients. Moreover, relationships are established between this algebra and multidimensional convolution operators, and a symbolic calculus is constructed for it. Also, necessary and sufficient conditions are obtained for the Fredholm property of operators from this algebra.
reviewed by: Ludwig Kohaupt
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 65J10
zbMATH DE Number: 6108825
zbMATH Keywords: integral operators
zbMATH Keywords: homogeneous kernels
zbMATH Keywords: convolution operators
zbMATH Keywords: boundedness
zbMATH Keywords: Fredholmness
MaRDI profile type: Publication
cites work: [Russian Text Ignored.]
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full work available at URL: s1066369x12070018
OpenAlex ID: W2026512753
description: scientific article; zbMATH DE number 6108825