Hardy spaces of vector-valued functions

A. V. Bukhvalov

doi:10.1007/bf02427716

journal article Jun 01, 1981

Hardy spaces of vector-valued functions

A. V. Bukhvalov

Journal of Soviet Mathematics Vol. 16 No. 3 pp. 1051-1059 · Springer Science and Business Media LLC

View at Publisher Save 10.1007/bf02427716

Topics

No keywords indexed for this article. Browse by subject →

References

20

[1]

A. V. Bukhvalov and G. Ya. Lozanovskii, “The representation of linear functionals and operators on vector lattices and certain applications of these representations,” Computer Center, Siberian Branch, Academy of Sciences of the USSR, School of the Theory of Operators in Functional Spaces (Aug. 25–31, 1975), Preprint, Novosibirsk, 1975.

[2]

B. Z. Vulikh, Introduction to the Theory of Partially Ordered Spaces, Wolters-Noordhoff, Groningen (1967).

[3]

N. Dunford and J. T. Schwartz, Linear Operators, Part I: General Theory, Wiley-Interscience, New York (1958).

[4]

A. V. Bukhvalov, “On the analytic representation of operators with an abstract norm,” Dokl. Akad. Nauk SSSR,208, No. 5, 1012–1015 (1973).

[5]

A. V. Bukhvalov, “On the analytic representation of operators with an abstract norm,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 11, 21–32 (1975).

[6]

K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs, New Jersey (1962).

[7]

S. Bochner and A. Taylor, “Linear functionals on certain spaces of abstractly valued functions,” Ann. Math.,39, 913–944 (1938). 10.2307/1968472

[8]

L. Schwartz, Analysis [Russian translation], Vol. 2, Mir, Moscow (1972).

[9]

S. Levi, “A note on Hardy spaces of vector-valued analytic functions,” Boll. Un. Mat. Ital., Ser. IV,5, 52–63 (1972).

[10]

R. Ryan, “The F. and M. Riesz theorem for vector measures,” Indag. Math.,25, No. 3, 408–412 (1963). 10.1016/s1385-7258(63)50041-9

[11]

R. Ryan, “Boundary values of analytic vector-valued functions,” Indag. Math.,24, No. 5, 558–572 (1962). 10.1016/s1385-7258(62)50056-5

[12]

Cl. Grossetete, “Sur certains classes de fonctions harmoniques dans le disque a valeur dans un espace vectoriel topologique localement convexe,” C. R. Acad. Sci. Paris,273, A1048-A1051 (1971).

[13]

Cl. Grossetete, “Classes de Hardy et de Nevanlinna pour les fonctions holomorphes a valeurs vectorielles,” C. R. Acad. Sci. Paris,274, A251-A253 (1972).

[14]

N. Dunford and J. T. Schwartz, Linears Operators, Part II: Spectral Theory, WileyInterscience, New York (1963).

[15]

A. Zygmund, Trigonometric Series, Vol. I, Cambridge Univ. Press, Cambridge (1959).

[16]

A. V. Bukhvalov, “On the duality of functors generated by spaces of vector-functions,” Izv. Akad. Nauk SSSR, Ser. Mat.,39, No. 6, 1284–1309 (1975).

[17]

B. S. Mityagin and A. S. Shvarts, “Functors in categories of Banach spaces,” Usp. Mat. Nauk,19, No. 2, 65–130 (1964).

[18]

D. P. Giesy and R. C. James, “Uniformly nonℓ(f) and β-convex Banach spaces,” Stud. Math.,48, No. 1, 61–69 (1973). 10.4064/sm-48-1-61-69

[19]

I. B. Bryskin and A. A. Sedaev, “On the geometric properties of the unit sphere in spaces of the type of Hardy classes,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,39, 7–16 (1974).

[20]

D. W. Boyd, “The Hilbert transform on rearrangement-invariant spaces,” Canad. J. Math.,19, 599–616 (1967). 10.4153/cjm-1967-053-7

Metrics

11

Citations

20

References

Details

Published: Jun 01, 1981
Vol/Issue: 16(3)
Pages: 1051-1059
License: View

Authors

A

A. V. Bukhvalov

Cite This Article

A. V. Bukhvalov (1981). Hardy spaces of vector-valued functions. Journal of Soviet Mathematics, 16(3), 1051-1059. https://doi.org/10.1007/bf02427716

Hardy spaces of vector-valued functions

You May Also Like