Singular Integral Equations in Special Weighted Spaces
2000 ◽
Vol 7
(4)
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pp. 633-642
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Keyword(s):
Abstract We prove the boundedness of the Cauchy singular integral operator in special weighted Sobolev and Hölder-Zygmund spaces for large values of the smoothness parameter, which is an integer m ≥ 0, when the underlying contour is piecewise-smooth with angular points and even with cusps. We obtain Fredholm criteria and an index formula for singular integral equations with piecewise-continuous coefficients and complex conjugation in the spaces and provided that the underlying contour has only angular points but no cusps. The Fredholm property and the index turn out to be independent of the smoothness parameter m.
1972 ◽
Vol 25
(4)
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pp. 369-402
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1989 ◽
Vol 26
(5)
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pp. 1194-1211
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2000 ◽
Vol 115
(1-2)
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pp. 283-300
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2010 ◽
Vol 371
(1)
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pp. 128-133
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2017 ◽
Vol 326
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pp. 268-272
1994 ◽
Vol 15
(2)
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pp. 285-297
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