Norms of the singular integral operator with Cauchy Kernel along certain contours |
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| Authors: | Israel Feldman Naum Krupnik Ilya Spitkovsky |
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| Institution: | (1) Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel;(2) Department of Mathematics, The College of William and Mary, 23187-8795 Williamsburg, Virginia, USA |
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| Abstract: | The norm of the above-mentioned operatorS is computed on the unions of parallel lines or concentric circles. The upper bound is found for its norm on the ellipse. In case of weighted spaces on the unit circle, the exact norm is found for some rational weights, and necessary and sufficient conditions on the weight are established, under which the essential norm ofS equals 1. |
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| Keywords: | Primary 47G10 Secondary 45P05 47B35 |
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