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Best Constants for the Riesz Projection

✍ Scribed by Brian Hollenbeck; Igor E. Verbitsky

Book ID
102593494
Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
176 KB
Volume
175
Category
Article
ISSN
0022-1236

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✦ Synopsis

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 ).) This was conjectured in 1968 by I. Gohberg and N. Krupnik.

We also prove an analogous inequality in the nonperiodic case where P + f =F &1 (/ R + Ff ) is the half-line Fourier multiplier on R. Similar weighted inequalities with sharp constants for L p (R, |x| : ), &1<:<p&1, are obtained. In the multidimensional case, our results give the norm of the half-space Fourier multiplier on R n .

πŸ“œ SIMILAR VOLUMES

to constants for Riesz projections
to constants for Riesz projections
✍ Jordi Marzo; Kristian Seip πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 French βš– 114 KB

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