Marcinkiewicz’s theorem on operator multipliers of Fourier series
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- by Milutin R. Dostanić PDF
- Proc. Amer. Math. Soc. 132 (2004), 391-396 Request permission
Abstract:
We give some sufficient conditions on the operators $A_{m}\!\in \!\mathcal {B} \left ( L^{p}\left ( 0,1\right ) \right )$ which for each $\Phi _{m}\in L^{p}\left ( 0,1\right )$ imply the inequality \[ \int \limits _{0}^{1}\int \limits _{0}^{2\pi }\left | \sum \limits _{m}e^{imx}\cdot A_{m}\Phi _{m}\left ( y\right ) \right | ^{p}dxdy\leq c_{p}^{p}\int \limits _{0}^{1}\int \limits _{0}^{2\pi }\left | \sum \limits _{m}e^{imx}\cdot \Phi _{m}\left ( y\right ) \right | ^{p}dxdy, \] $1<p<\infty .$References
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Additional Information
- Milutin R. Dostanić
- Affiliation: Matematicki Fakultet, University of Belgrade, Studentski Trg 16, 11000 Belgrade, Serbia
- Email: domi@matf.bg.ac.yu
- Received by editor(s): July 19, 2001
- Received by editor(s) in revised form: September 20, 2002
- Published electronically: June 11, 2003
- Communicated by: Joseph A. Ball
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 391-396
- MSC (2000): Primary 42B15
- DOI: https://doi.org/10.1090/S0002-9939-03-07017-5
- MathSciNet review: 2022361