×

On the problem of classification of Banach algebras of singular integral operators with PC-coefficients in \(L_p\) spaces on composite contours. (English. Russian original) Zbl 0928.47037

Funct. Anal. Appl. 32, No. 3, 212-214 (1998); translation from Funkts. Anal. Prilozh. 32, No. 3, 87-90 (1998).
It is shown that the dimension of the values and the degree of integrability of the functions together with the topological structure of the underlying contours essentially characterize the Banach algebras in the title. Certain weights seem to be irrelevant.

MSC:

47G10 Integral operators
47B38 Linear operators on function spaces (general)
46H05 General theory of topological algebras
47L80 Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] V. M. Deundyak, I. B. Simonenko, and V. A. Stukopin, Funkts. Anal. Prilozhen.,27, No. 4, 69–71 (1993).
[2] L. Hörmander, Acta Math.,104, 93–140 (1960). · Zbl 0093.11402 · doi:10.1007/BF02547187
[3] Ch. Fefferman and I. Stein, Acta Math.,129, 137–193 (1972). · Zbl 0257.46078 · doi:10.1007/BF02392215
[4] I. Hirshman, Duke Math. J.,26, 221–242 (1959). · Zbl 0085.09201 · doi:10.1215/S0012-7094-59-02623-7
[5] I. B. Simonenko and Chin Ngok Min, A Local Method in the Theory of One-Dimensional Singular Integral Operators with Piecewise Continuous Coefficients. The Fredholm property [in Russian], Rostov State University, Rostov-na-Donu (1986). · Zbl 0623.45008
[6] V. M. Deundyak, I. B. Simonenko, and V. A. Stukopin, Integral’nye i Diff. Uravneniya, KGU, Elista, 1993, pp. 35–47.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.