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Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
Introduction...................................................................................................5
0. Preliminaries................................................................................................7
1. Fundamental properties of harmonic vector functions...............................13
2. Hardy spaces of vector functions...............................................................15
Relations between scalar and vector Hardy classes...................................15
The factorization theorem for $H^p(𝔻,X)$...................................................19
Nontangential limits of functions in $h^p(𝔻,X)$...........................................22
Properties of functions in $h^p(𝕋,X)$..........................................................27
3. Spaces $h^p(𝔻,X)$ and $M_p(𝕋,X)$..........................................................29
4. The sets of translates of harmonic functions..............................................33
5. Translations of functions from Hardy classes..............................................37
6. Translations of functions from Smirnov classes...........................................41
7. Translations of measures from $M_p(G,X)$................................................43
8. A criterion of uncomplementability of $L^p(λ_G,X)$ in $M_p(G,X)$.............53
9. Pettis integrability of the translation function for vector measures...............64
References...................................................................................................77
Introduction...................................................................................................5
0. Preliminaries................................................................................................7
1. Fundamental properties of harmonic vector functions...............................13
2. Hardy spaces of vector functions...............................................................15
Relations between scalar and vector Hardy classes...................................15
The factorization theorem for $H^p(𝔻,X)$...................................................19
Nontangential limits of functions in $h^p(𝔻,X)$...........................................22
Properties of functions in $h^p(𝕋,X)$..........................................................27
3. Spaces $h^p(𝔻,X)$ and $M_p(𝕋,X)$..........................................................29
4. The sets of translates of harmonic functions..............................................33
5. Translations of functions from Hardy classes..............................................37
6. Translations of functions from Smirnov classes...........................................41
7. Translations of measures from $M_p(G,X)$................................................43
8. A criterion of uncomplementability of $L^p(λ_G,X)$ in $M_p(G,X)$.............53
9. Pettis integrability of the translation function for vector measures...............64
References...................................................................................................77
Słowa kluczowe
Tematy
Kategoryzacja MSC:
- 28C10: Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
- 46B22: Radon-Nikod{\'y}m, Kre{\u\i}n-Milman and related properties
- 46E40: Spaces of vector- and operator-valued functions
- 46B20: Geometry and structure of normed linear spaces
- 46B03: Isomorphic theory (including renorming) of Banach spaces
- 32A35: H p -spaces, Nevanlinna spaces
- 46J15: Banach algebras of differentiable or analytic functions, H p -spaces
- 46E27: Spaces of measures
- 46G10: Vector-valued measures and integration
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
359
Liczba stron
79
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCLIX
Daty
wydano
1996
otrzymano
1995-07-13
poprawiono
1996-02-12
Twórcy
autor
- Faculty of Mathematics and Computer Sciences, A. Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland
Bibliografia
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- [D-E] L. Drewnowski and G. Emmanuele, The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of c₀, ibid. 104 (1993), 111-123.
- [E] G. Emmanuele, Some more Banach spaces for which complementability of spaces of Bochner integrable functions in spaces of vector measures occurs, preprint.
- [Du] P. L. Duren, Theory of $H^p$-Spaces, Pure Appl. Math. 38, Academic Press, New York, 1970.
- [D-S] N. Dunford and J. Schwartz, Linear Operators, Part 1, Interscience Publ., New York, 1958.
- [F-T] D. H. Fremlin and M. Talagrand, A decomposition theorem for additive set-functions, with applications to Pettis integral and ergodic means, Math. Z. 168 (1979), 117-142.
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- [Gar] J. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981.
- [Gr-1] C. Grossetête, Sur certaines classes de fonctions harmoniques dans le disque à valeurs dans un espace vectoriel topologique localement convexe, C. R. Acad. Sci. Paris Sér. A 273 (1971), 1048-1051.
- [Gr-2] C. Grossetête, Classes de Hardy et de Nevanlinna pour les fonctions holomorphes à valeurs vectorielles, ibid. 274 (1972), 251-253.
- [Hal] P. R. Halmos, Measure Theory, Van Nostrand, New York, 1950.
- [H-L] G. H. Hardy and J. E. Littlewood, Some properties of conjugate functions, J. Reine Angew. Math. 167 (1932), 405-423.
- [He] M. Heins, Vector valued harmonic functions, in: Functions, Series, Operators, Vol. 1, Colloq. Math. Soc. János Bolyai 35, North-Holland, 1983, 621-632.
- [H-R] F. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. 1, Grundlehren Math. Wiss. 150, Springer, 1978.
- [H-P] E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups, Colloq. Publ. 31, Amer. Math. Soc., Providence, R.I., 1957.
- [Ho] J. Hoffmann-Jοrgensen, Sums of independent Banach space valued random variables, Studia Math. 52 (1974), 159-186.
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- [K-P-R] N. J. Kalton, N. T. Peck and J. W. Roberts, An F-space Sampler, London Math. Soc. Lecture Note Ser. 89, Cambridge Univ. Press, 1984.
- [Ko] P. Koosis, Introduction to Hₚ Spaces, London Math. Soc. Lecture Note Ser. 40, Cambridge Univ. Press, 1980.
- [Kw] S. Kwapień, On Banach spaces containing c₀. A supplement to the paper by Hoffmann-Jοrgensen "Sums of independent Banach space valued random variables", Studia Math. 52 (1974), 187-188.
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- [M-1] K. Musiał, The weak Radon-Nikodym property in Banach spaces, ibid. 64 (1979), 151-173.
- [M-2] K. Musiał, Topics in the theory of Pettis integration, Rend. I.M.U. Trieste 23 (1991), 177-262.
- [Nam] I. Namioka, Neighborhoods of extreme points, Israel J. Math. 5 (1967), 145-152.
- [Naw-1] M. Nawrocki, The Fréchet envelopes of vector-valued Smirnov classes, Studia Math. 94 (1989), 61-75.
- [Naw-2] M. Nawrocki, Duals of vector-valued $H^p$-spaces for 0 < p < 1, Indag. Math. 2 (1991), 233-241.
- [Pie] A. Pietsch, Operator Ideals, Deutscher Verlag Wiss., Berlin, 1978.
- [Pis] G. Pisier, Une propriété de stabilité de la classe des espaces ne contenant pas l₁, C. R. Acad. Sci. Paris Sér. A 285 (1978), 747-749.
- [Ri] W. J. Ricker, Characterization of Poisson integrals of vector valued functions and measures on the unit circle, Hokkaido Math. J. 16 (1987), 29-42.
- [R-S] L. H. Riddle and E. Saab, On functions that are universally Pettis integrable, Illinois J. Math. 29 (1985), 509-531.
- [Ros-1] H. P. Rosenthal, Projections onto translation-invariant subspaces of $L^p(G)$, Mem. Amer. Math. Soc. 63 (1966).
- [Ros-2] H. P. Rosenthal, On factors of C([0,1]) with nonseparable dual, Israel J. Math. 13 (1972), 361-378.
- [Ru-1] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1974.
- [Ru-2] W. Rudin, Function Theory in the Unit Ball of ℂⁿ, Springer, Berlin, 1981.
- [Ru-3] W. Rudin, Homomorphisms and translations in $L^∞(G)$, Adv. in Math. 16 (1975), 72-90.
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- [Sw] L. Schwartz, Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures, Oxford Univ. Press, 1973.
- [Sin] I. Singer, Linear functionals on the space of continuous functions from a compact Hausdorff space into a Banach space, Rev. Math. Pures Appl. 3 (1957), 201-215 (in Russian).
- [Ta-1] M. Talagrand, Pettis integral and measure theory, Mem. Amer. Math. Soc. 307 (1984).
- [Ta-2] M. Talagrand, Convex hull of sets of measurable functions, Riemann measurable functions and measurability of translations, Ann. Inst. Fourier (Grenoble) 32 (1982), 39-69.
- [W] P. Wojtaszczyk, Banach Spaces for Analysts, Cambridge Univ. Press, Cambridge, 1991.
Języki publikacji
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Uwagi
1991 Mathematics Subject Classification: Primary 46E40, 46E27, 46B20, 46B22, 46G10; Secondary 46B03, 28C10, 46J15, 32A35
Identyfikator YADDA
bwmeta1.element.zamlynska-1daf756d-fb23-4b44-833d-0876d0dbb61a
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ISSN
0012-3862
Kolekcja
DML-PL
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