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Bukhvalov, A. V.; Danilevich, A. A.

Boundary properties of analytic and harmonic functions with values in Banach space. (English. Russian original) Zbl 0496.30029

Math. Notes 31, 104-110 (1982); translation from Mat. Zametki 31, 203-214 (1982).
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Cited in 11 Reviews
Cited in 61 Documents

MSC:

30D55 \(H^p\)-classes (MSC2000)
30E25 Boundary value problems in the complex plane

Keywords:

Hardy spaces; boundary values; analytic and harmonic functions; Banach space
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References:

[1] A. V. Bukhvalov, ?Hardy spaces of vector-valued functions,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,65, 5-16 (1976). · Zbl 0345.46035
[2] A. A. Danilevich, ?Some boundary properties of abstract analytic functions, and their applications,? Mat. Sb.,100, No. 4, 507-533 (1976).
[3] R. Ryan, ?Boundary values of analytic vector valued functions,? Proc. Koninkl. Nederl. Acad.,A65, No. 5, 558-572 (1962). · Zbl 0127.07001
[4] A. A. Danilevich, ?The theory of bounded analytic functions,? Sb. Mat. Anal. Teor. Funktsii,3, Izd. Mosk. Obl. Pedagog. Inst., 1-211 (1974).
[5] C. Grossetete, ?Sur certaines classes de fonctions harmoniques dans le disque a valeur dans un espace vectoriel topologique localement convexe,? C.R. Acad. Sci. Paris,A273, No. 22, A1048-A1051 (1971).
[6] L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1977). · Zbl 0127.06102
[7] A. V. Bukhvalov, ?Spaces with mixed norm,? Vestn. Leningr. Gos. Univ., No. 19, 5-12 (1973). · Zbl 0277.46024
[8] S. D. Chatterji, ?Martingale convergence and the Radon-Nikodim theorem in Banach spaces,? Math. Scand.,22, 21-41 (1968). · Zbl 0175.14503
[9] S. Bochner and A. E. Taylor, ?Linear functionals on certain spaces of abstractly valued functions,? Ann. Math. (2),39, 913-944 (1938). · Zbl 0020.37101 · doi:10.2307/1968472
[10] A. V. Bukhvalov, ?The analytic representation of linear operators using measurable vector-functions,? Izv. Vyssh. Uchebn. Zaved., Mat., No. 7, 21-31 (1977).
[11] A. Zygmund, Trigonometrical Series, Vol. 2, Cambridge Univ. Press. · Zbl 0011.01703
[12] A. Pelezynski, ?Banach spaces of analytic functions and absolutely summing operators,? CBMS Reg. Conf. Ser. in Math.,30, 91 (1977).
[13] V. P. Khavin, ?The spaces H? and L1/H 0 1 ,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,39, 120-148 (1974). · Zbl 0358.46036
[14] T. Figiel, W. B. Johnson, and L. Tzafriri, ?On Banach lattices and spaces, having local unconditional structure, with applications to Lorentz function spaces,? J. Appr. Theory,13, No. 4, 395-412 (1975). · Zbl 0307.46007 · doi:10.1016/0021-9045(75)90023-4
[15] W. B. Johnson and L. Tzafriri, ?Some more Banach spaces which do not have local unconditional structure,? Houston J. Math.,3, No. 1, 55-60 (1977). · Zbl 0343.46014
[16] K. Huffman, Banach Spaces of Analytic Functions, Prentice-Hall (1962). · Zbl 0137.13702
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