Critical points of essential norms of singular integral operators in weighted spaces |
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Authors: | Naum Krupnik Yafim Spigel |
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Institution: | (1) Dept. of Math. and CS, Bar-Ilan University, 52900 Ramat-Gan, Israel;(2) Holon Center for Technological Education, P.O.B. 305, 58102 Holon, Israel |
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Abstract: | We show that for any simple piecewise Ljapunov contour there exists a power weight such that the essential norm |S
| in the spaceL
2( , ) does not depend on the angles of the contour and it is given by formula (2). All such weights are described. For the union = 1![cup](/content/g73nj8v4178k03w0/xxlarge8746.gif) 2 of two simple piecewise Lyapunov curves we prove that the essential norm |S
| inL
2( ) is minimal if both 1 and 2 are smooth in some neighborhoods of the common points. It is the case when the norm |S
| in the spaceL
2( ) as well as inL
2( , ) does not depend on the values of the angles and it can be calculated by formula (5). |
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Keywords: | 47G10 |
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