Geodesic
Multiplication Invariant Subspaces of Hardy Spaces
Canadian journal of mathematics, Tome 49 (1997) no. 1, pp. 100-118

Voir la notice de l'article provenant de la source Cambridge University Press

This paper studies closed subspaces L of the Hardy spaces Hp which are g-invariant (i.e., g. L ⊆ L) where g is inner, g ≠ 1. If p = 2, theWold decomposition theorem implies that there is a countable “g-basis” f1, f2, . . . of L in the sense that L is a direct sum of spaces fj . H2[g] where H2[g] = {f o g | f ∈ H2}. The basis elements fj satisfy the additional property that ∫T |fj|2gk = 0, k = 1, 2, . . . . We call such functions g-2-inner. It also follows that any f ∈ H2 can be factored f = hf ,2 . (F2 o g) where hf,2 is g-2-inner and F is outer, generalizing the classical Riesz factorization. Using Lp estimates for the canonical decomposition of H2,we find a factorization f = hf ,p.(Fpog) for f ∈ Hp. If p ≤ 1 and g is a finite Blaschke product we obtain, for any g-invariant L ⊆ Hp, a finite g-basis of g-p-inner functions.
DOI : 10.4153/CJM-1997-005-9
Mots-clés : 30H05, 46E15, 47B38 
Lance, T. L.; Stessin, M. I. Multiplication Invariant Subspaces of Hardy Spaces. Canadian journal of mathematics, Tome 49 (1997) no. 1, pp. 100-118. doi: 10.4153/CJM-1997-005-9
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1997-005-9/}
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