@article{9499af90c0fc4b4a839bf32b24ef64d7,
title = "A Kato-Yau inequality and decay estimate for eigenspinors",
abstract = "We show that harmonic spinors obey a strengthened version of the well-known pointwise Kato inequality for sections of a vector bundle with a connection. We then give two different proofs an interesting decay estimate for harmonic spinors, one using our Kato-Yau estimate and resulting differential inequality, and a second using known eigenvalue calculations for the Dirac operator on the three-sphere. As an example of the use of these estimates, we also describe some new applications to the problems of gluing and ungluing PU(2) monopoles.",
keywords = "Dirac operator, Kato-Yao inequality, decay estimate, harmonic spinor",
author = "Feehan, {Paul M.N.}",
note = "Funding Information: Math Subject Classifications. Primary: 58G03. Secondary: 53C07, 58G18, 58G25, 35F05. Key Words and Phrases. Dirac operator, harmonic spinor, decay estimate, Kato-Yao inequality. Acknowledgements and Notes. The author was supported in part by NSF grant DMS 9704174 and, through the Institute for Advanced Study (1998-1999), by NSF grant DMS 9729992. Funding Information: I am grateful to Tom Mrowka for pointing out that calculations of the Dirac operator spectrum for S 3 are well-known and that such calculations can be found in \[22\].I am also grateful to Hiraku Nakajima for directing me to the references \[4\]a nd \[26\]a nd to Deane Yang for describing the early use of Kato-Yau type differential inequalities in harmonic analysis \[30, Section VII.3.1\]. Finally, I would like to thank the Institute for Advanced Study, Princeton, and the National Science Foundation, for their generous support during the preparation of this article.",
year = "2001",
doi = "10.1007/BF02922015",
language = "English (US)",
volume = "11",
pages = "469--489",
journal = "Journal of Geometric Analysis",
issn = "1050-6926",
publisher = "Springer New York",
number = "3",
}