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On a maximum principle for pseudocontinuable functions. / Александров, Алексей Борисович.
в: Journal of Mathematical Sciences , Том 85, № 2, 1997, стр. 1767-1772.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - On a maximum principle for pseudocontinuable functions
AU - Александров, Алексей Борисович
PY - 1997
Y1 - 1997
N2 - Let Θ be an inner function and let α ∈ ℂ, |α| = 1. Denote by σα the nonnegative singular measure whose Poisson integral is equal to Re α+Θ/α-Θ. A theorem of Clark provides a natural unitary operator Uα that identifies H2 ⊖ ΘH2 with L 2(σα). The following fact is established. Assume that f ∈ H2 ⊖ ΘH2, 2 < p ≤ + ∞, α ≠ β. Then ∥f∥Hp ≤ C(α,β,p)(∥Uα f∥Lp(σα) + ∥Uβf∥Lp(σβ)).
AB - Let Θ be an inner function and let α ∈ ℂ, |α| = 1. Denote by σα the nonnegative singular measure whose Poisson integral is equal to Re α+Θ/α-Θ. A theorem of Clark provides a natural unitary operator Uα that identifies H2 ⊖ ΘH2 with L 2(σα). The following fact is established. Assume that f ∈ H2 ⊖ ΘH2, 2 < p ≤ + ∞, α ≠ β. Then ∥f∥Hp ≤ C(α,β,p)(∥Uα f∥Lp(σα) + ∥Uβf∥Lp(σβ)).
UR - http://www.scopus.com/inward/record.url?scp=53249090468&partnerID=8YFLogxK
U2 - 10.1007/BF02355285
DO - 10.1007/BF02355285
M3 - Article
AN - SCOPUS:53249090468
VL - 85
SP - 1767
EP - 1772
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
SN - 1072-3374
IS - 2
ER -
ID: 87313016