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On the existence of nontangential boundary values of pseudocontinuable functions. / Александров, Алексей Борисович.
в: Journal of Mathematical Sciences , Том 87, № 5, 1997, стр. 3781-3787.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - On the existence of nontangential boundary values of pseudocontinuable functions
AU - Александров, Алексей Борисович
N1 - Funding Information: Proof. Without loss of generality, we may assume that/z = IIE.a~, where lIE is the characteristic function of a Borel set E C T. It was proved in \[15\t]h at the identity embedding operator 0*(H 2) C 0*(H P) is compact. Consequently, so is the embedding operator 0*(/'/2) ~ Lo(/z). From the Clark theorem \[8\]q uoted above we deduce that the operator f ~-* f\[E acting from L2(a~) to L~ is compact. Now it is clear that # is discrete. \[\] I am grateful to Max-Planck-Arbeitsgruppe "Algebraische Geometric und Zahlentheorie," during the stay at which this work was finished. This research was supported in part by the Russian Foundation for Fundamental Studies, grant 94-01-0132, and by the International Science Foundation, grant R3M000.
PY - 1997
Y1 - 1997
N2 - Let θ be an inner function, let θ*(H2) = H2 Θ θH2, and let p be a finite Borel measure on the unit circle double-struck T sign. Our main purpose is to prove that, if every function f ∈ θz.ast;(H2) can be defined μ-almost everywhere on double-struck T sign in a certain (weak) natural sense, then every function f ∈ θ*(H2) has finite angular boundary values μ-almost everywhere on double-struck T sign. A similar result is true for the Lp-analog of θ*(H2) (p > 0).
AB - Let θ be an inner function, let θ*(H2) = H2 Θ θH2, and let p be a finite Borel measure on the unit circle double-struck T sign. Our main purpose is to prove that, if every function f ∈ θz.ast;(H2) can be defined μ-almost everywhere on double-struck T sign in a certain (weak) natural sense, then every function f ∈ θ*(H2) has finite angular boundary values μ-almost everywhere on double-struck T sign. A similar result is true for the Lp-analog of θ*(H2) (p > 0).
UR - http://www.scopus.com/inward/record.url?scp=53249115556&partnerID=8YFLogxK
U2 - 10.1007/BF02355824
DO - 10.1007/BF02355824
M3 - Article
AN - SCOPUS:53249115556
VL - 87
SP - 3781
EP - 3787
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
SN - 1072-3374
IS - 5
ER -
ID: 87312768