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to constants for Riesz projections

✍ Scribed by Jordi Marzo; Kristian Seip

Book ID
104006158
Publisher
Elsevier Science
Year
2011
Tongue
French
Weight
114 KB
Volume
135
Category
Article
ISSN
0007-4497

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✦ Synopsis

The norm of the Riesz projection from L ∞ (T n ) to L p (T n ) is considered. It is shown that for n = 1, the norm equals 1 if and only if p 4 and that the norm behaves asymptotically as p/(Ο€e) when p β†’ ∞. The critical exponent p n is the supremum of those p for which the norm equals 1. It is proved that 2 + 2/(2 n -1) p n < 4 for n > 1; it is unknown whether the critical exponent for n = ∞ exceeds 2.

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We prove the following inequality with a sharp constant, where 1<p< , and P + : L p (T) Γ„ H p (T) is the Riesz projection onto the Hardy space H p (T) on the unit circle T. (In other words, the ``angle'' between the analytic and co-analytic subspaces of L p (T) equals ?Γ‚p\* where p\*=max ( p, p p&1

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## Abstract The Dirac operators equation image with __L__^2^‐potentials equation image considered on [0, Ο€] with periodic, antiperiodic or Dirichlet boundary conditions (__bc__), have discrete spectra, and the Riesz projections equation image are well‐defined for |__n__ | β‰₯ __N__ if __N__ is