Boundary values, integral transforms, and growth of vector valued Hardy functions
Аутори
Carmichael, Richard D.Pilipović, Stevan
Vindas, Jasson
Остала ауторства
Milovanović, Gradimir V.Конференцијски прилог (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
Banach space valued Hardy functions Hp, 0 < p ≤ ∞, are defined
with the functions having domain in tubes T C = Rn + iC ⊂ Cn; H2 functions with values
in Hilbert space are characterized as Fourier-Laplace transforms of functions which satisfy
a certain norm growth property. These H2 functions are shown to equal a Cauchy integral
when the base C of the tube T C is specialized. For certain Banach spaces and certain bases
C of the tube T C , all Hp functions, 1 ≤ p ≤ ∞, are shown to equal the Poisson integral of
Lp functions, have boundary values in Lp norm on the distinguished boundary Rn + i{0} of
the tube T C , and have pointwise growth properties. For H2 functions with values in Hilbert
space we show the existence of L2 boundary values on the topological boundary Rn + i ∂C
of the tube T C .
Кључне речи:
Hardy functions / vector valued analytic functions / integral transforms / boundary values in Lp normИзвор:
Bulletin T.CLIV de l’Académie serbe des sciences et des arts, 2021, 115-129Издавач:
- Beograd : Académie Serbe des sciences et des arts
Напомена:
- Bulletin t. 154 de l'Académie serbe des sciences et des arts. Classe des sciences mathématiques et naturelles. Sciences mathematiques no 46
TY - CONF AU - Carmichael, Richard D. AU - Pilipović, Stevan AU - Vindas, Jasson PY - 2021 UR - https://dais.sanu.ac.rs/123456789/13286 AB - Banach space valued Hardy functions Hp, 0 < p ≤ ∞, are defined with the functions having domain in tubes T C = Rn + iC ⊂ Cn; H2 functions with values in Hilbert space are characterized as Fourier-Laplace transforms of functions which satisfy a certain norm growth property. These H2 functions are shown to equal a Cauchy integral when the base C of the tube T C is specialized. For certain Banach spaces and certain bases C of the tube T C , all Hp functions, 1 ≤ p ≤ ∞, are shown to equal the Poisson integral of Lp functions, have boundary values in Lp norm on the distinguished boundary Rn + i{0} of the tube T C , and have pointwise growth properties. For H2 functions with values in Hilbert space we show the existence of L2 boundary values on the topological boundary Rn + i ∂C of the tube T C . PB - Beograd : Académie Serbe des sciences et des arts C3 - Bulletin T.CLIV de l’Académie serbe des sciences et des arts T1 - Boundary values, integral transforms, and growth of vector valued Hardy functions SP - 115 EP - 129 UR - https://hdl.handle.net/21.15107/rcub_dais_13286 ER -
@conference{ author = "Carmichael, Richard D. and Pilipović, Stevan and Vindas, Jasson", year = "2021", abstract = "Banach space valued Hardy functions Hp, 0 < p ≤ ∞, are defined with the functions having domain in tubes T C = Rn + iC ⊂ Cn; H2 functions with values in Hilbert space are characterized as Fourier-Laplace transforms of functions which satisfy a certain norm growth property. These H2 functions are shown to equal a Cauchy integral when the base C of the tube T C is specialized. For certain Banach spaces and certain bases C of the tube T C , all Hp functions, 1 ≤ p ≤ ∞, are shown to equal the Poisson integral of Lp functions, have boundary values in Lp norm on the distinguished boundary Rn + i{0} of the tube T C , and have pointwise growth properties. For H2 functions with values in Hilbert space we show the existence of L2 boundary values on the topological boundary Rn + i ∂C of the tube T C .", publisher = "Beograd : Académie Serbe des sciences et des arts", journal = "Bulletin T.CLIV de l’Académie serbe des sciences et des arts", title = "Boundary values, integral transforms, and growth of vector valued Hardy functions", pages = "115-129", url = "https://hdl.handle.net/21.15107/rcub_dais_13286" }
Carmichael, R. D., Pilipović, S.,& Vindas, J.. (2021). Boundary values, integral transforms, and growth of vector valued Hardy functions. in Bulletin T.CLIV de l’Académie serbe des sciences et des arts Beograd : Académie Serbe des sciences et des arts., 115-129. https://hdl.handle.net/21.15107/rcub_dais_13286
Carmichael RD, Pilipović S, Vindas J. Boundary values, integral transforms, and growth of vector valued Hardy functions. in Bulletin T.CLIV de l’Académie serbe des sciences et des arts. 2021;:115-129. https://hdl.handle.net/21.15107/rcub_dais_13286 .
Carmichael, Richard D., Pilipović, Stevan, Vindas, Jasson, "Boundary values, integral transforms, and growth of vector valued Hardy functions" in Bulletin T.CLIV de l’Académie serbe des sciences et des arts (2021):115-129, https://hdl.handle.net/21.15107/rcub_dais_13286 .