Abstract
We describe dual spaces of classes of the Hardy–Sobolev type \(F_l^{pq} (U^n )\) of functions holomorphic in a polydisk for 0 < p ≤ 1 and q ∈ (0, ∞) and for p ∈ (1, ∞) and q = 1.
Similar content being viewed by others
REFERENCES
C. Fefferman and E. Stein, “H p spaces of several variables,” Acta Math. 192, 137–173 (1972).
S. V. Shvedenko, “Hardy classes and related spaces of analytic functions in a unit disk, polydisk, and ball,” in: VINITI Series in Mathematics [in Russian], Vol. 23, VINITI, Moscow (1985), pp. 3–124.
A. Djrbashian and F. Shamoian, “Topics in the theory of A p ? spaces,” Teubner-Texte Math., 105, 200 (1988).
M. Yevtic and M. Pavlovic, “Coefficient multipliers on spaces of analytic functions,” Acta Sci. Math.,64, 531–545 (1998).
S. M. Buckley, P. Koskela, and D. Vucoti¢, “Fractional integration, differentiation and weighted Bergman spaces,” Cambridge Phil. Soc.,?No. 2, 377–385 (1999).
H. Triebel, Theory of Function Spaces, Akademische Verlagsgeselleschaft, Leipzig (1983).
I. E. Verbitskii, Imbedding Theorems for Spaces of Analytic Functions with Mixed Norm ?[in Russian], Preprint No. 44, Institute of Geography and Geology, Kishinev (1987).
V. S. Guliev and P. I. Lizorkin, “Classes of holomorphic and harmonic functions in a polydisk in connection with their boundary values,” Tr.Mat.Inst.Ross.Akad.Nauk, 204, 137–159 (1993).
J. Ortega and J. Fabrega, “Holomorphic Triebel – Lizorkin spaces,” J.Function. Anal.,151, 177–212 (1997).
J. Ortega and J. Fabrega, “Hardy's inequality and embeddings in holomorphic Triebel – Lizorkin spaces. III,” J. Math.,43, No. 4, 733–751 (1999).
R. F. Shamoyan, “Continuous functionals and multipliers of power series of a class of functions holomorphic in a polydisk,” Izv. Vyssh. Uchebn. Zaved.,Ser. Mat. ??No. 7, 67–69 (2000).
R. F. Shamoyan, “On the multipliers from a space of the Bergman type into Hardy spaces in a polydisk,” Urk. Mat. Zh., 52, No. 12, 1405–1415 (2000).
J. B. Garnett, Bounded Analytic Functions, Academic Press, Orlando (1981).
A. B. Aleksandrov, “Theory of functions in a ball,” in: VINITI Series in Contemporary Problems in Mathematics [in Russian], Vol. 8, VINITI, Moscow (1985), pp. 115–186.
G. M. Fikhtengol'ts, Course in Differential and Integral Calculus [in Russian], Vol. 3, Nauka, Moscow (1970).
M. I. Gvaradze, “Multipliers of one class of analytic functions defined on a polydisk,” Tr. Tbilisi Mat. Inst., 66, 15–21 (1980).
W. Rudin, Funtion Theory in Polydiscs, Benjamin, New York (1969).
P. Koosis, Introduction to H p Spaces. With an Appendix on Wolff's Proof of the Corona Theorem, Cambridge University Press, Cambridge (1980).
P. L. Duren, Theory of H p Spaces, Academic Press, New York (1970).
A. B. Aleksandrov, “Essays on non locally convex Hardy classes,” Complex Anal.Spectral Theory:Lect. Notes Math., 844, 1–90 (1981).
R. F. Shamoyan and O. V. Yaroslavtseva, “Continuous projectors, duality, and diagonal mapping in weighted spaces of holomorphic functions with mixed norm,” Zap. Nauchn. Sem. POMI, 247, 268–276 (1997).?
Rights and permissions
About this article
Cite this article
Shamoyan, R.F. On the Representation of Linear Continuous Functionals in Spaces of Analytic Functions of the Hardy–Sobolev Type in a Polydisk. Ukrainian Mathematical Journal 55, 812–831 (2003). https://doi.org/10.1023/B:UKMA.0000010258.47983.00
Issue Date:
DOI: https://doi.org/10.1023/B:UKMA.0000010258.47983.00