Fourier multipliers on weighted $L^p$-spaces
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- by T. S. Quek PDF
- Proc. Amer. Math. Soc. 127 (1999), 2343-2351 Request permission
Abstract:
In his 1986 paper in the Rev. Mat. Iberoamericana, A. Carbery proved that a singular integral operator is of weak type $(p,p)$ on $L^{p}(\mathbb {R}^{n})$ if its lacunary pieces satisfy a certain regularity condition. In this paper we prove that Carbery’s result is sharp in a certain sense. We also obtain a weighted analogue of Carbery’s result. Some applications of our results are also given.References
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Additional Information
- T. S. Quek
- Affiliation: Department of Mathematics, National University of Singapore, Singapore 119260, Republic of Singapore
- Email: matqts@leonis.nus.edu.sg
- Received by editor(s): August 20, 1996
- Received by editor(s) in revised form: October 31, 1997
- Published electronically: April 9, 1999
- Communicated by: J. Marshall Ash
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2343-2351
- MSC (1991): Primary 42A45
- DOI: https://doi.org/10.1090/S0002-9939-99-04812-1
- MathSciNet review: 1486747
Dedicated: Dedicated to Professor Leonard Y. H. Yap on the ocassion of his sixtieth birthday