Abstract
We show that the difference between the Bergman and Szegö projections on a smooth, bounded planar domain gains a derivative in the L p-Sobolev and Lipschitz spaces.
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Bell, S.: The Cauchy Transform, Potential Theory, and Conformal Mapping. CRC Press, Boca Raton (1992)
Boutet de Monvel, L., Sjöstrand, J.: Sur la singularité des noyaux de Bergman et de Szegö. Soc. Math. Fr. Astérisque 34–35, 123–164 (1976)
Kerzman, N., Stein, E.M.: The Cauchy kernel, the Szegö kernel, and Riemann mapping function. Math. Ann. 236, 85–93 (1978).
Koenig, K.D.: Comparing the Bergman and Szegö projections on domains with subelliptic boundary Laplacian. Math. Ann. 339, 667–693 (2007)
Lanzani, L., Stein, E.M.: Szegö and Bergman projections on non-smooth planar domains. J. Geom. Anal. 14, 63–86 (2004)
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Communicated by Jeffery McNeal.
Research supported in part by NSF Grant DMS-0457500.
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Koenig, K.D. An Analogue of the Kerzman-Stein Formula for the Bergman and Szegö Projections. J Geom Anal 19, 81–86 (2009). https://doi.org/10.1007/s12220-008-9051-x
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DOI: https://doi.org/10.1007/s12220-008-9051-x