On Banach envelopes of Hardy-Orlicz spaces on planar domains

• Autorzy: Rzeczkowski M.

Identyfikatory

DOI

10.14708/cm.v58i1-2.6408

• Języki publikacji: EN

Abstrakty

EN

We investigate Hardy-Orlicz spaces and weighted Bergman spaces on multiply connected domains and describe Banach envelopes of Hardy-Orlicz spaces generated by Orlicz functions well estimated by power-type functions.

Słowa kluczowe

EN

Hardy-Orlicz spaces; Banach envelope; Hardy spaces on planar domains

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2018
• Tom: Vol. 58, No. 1/2
• Strony: 79--92
• Opis fizyczny: Bibliogr. 19 poz., rys.

Twórcy

autor

Rzeczkowski M.

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

Bibliografia

• [1] D. M. Boyd, The metric space Hp (A), 0 < p < 1, and its containing Banach space, Colloq. Math. 40 (1978/79), no. 1, 119-129.
• [2] J. B. Conway, Functions of one complex variable. I, Springer, New York 1978.
• [3] J. B. Conway, Functions of one complex variable. II, Springer, New York 1996.
• [4] P. L. Duren, Theory of Hp spaces, Academic Press, New York 1970.
• [5] P. L. Duren, B. W. Romberg, and A. L. Shields, Linear functionals on Hp spaces with 0 < p < 1, J. Reine Angew. Math. 238 (1969), 32-60, DOI 10.1515/crll.1969.238.32.
• [6] S. D. Fisher, Function theory on planar domains, Wiley, New York 1983.
• [7] J. B. Garnett and D. E. Marshall, Harmonic measure, Cambridge University Press, Cambridge 2005.
• [8] P. Lefevre, D. Li, H. Queffélec, and L. Rodriguez-Piazza, Composition operators on Hardy-Orlicz spaces, Mem. Amer. Math. Soc. 207 (974) (2010).
• [9] M. Mastyło and P. Mleczko, Solid hulls of quasi-Banach spaces of analytic functions and interpolation, Nonlinear Anal. 73 (2010), no. 1, 84-98, DOI 10.1016/j.na.2010.02.043.
• [10] W. Matuszewska, Regularly increasing functions in connection with the theory of L*φ-spaces, Studia Math. 21 (1962), 317-344.
• [11] A. Michalak and M. Nawrocki, Banach envelopes of vector valued Hp spaces, Indag. Math. (N.S.) 13 (2002), no. 2, 185-195, DOI 10.1016/s0019-3577(02)80004-0.
• [12] J. Musielak, Orlicz spaces and modular spaces, Lecture Notes in Mathematics, vol. 1034, Springer-Verlag, Berlin Heidelberg 1983, DOI 10.1007/bfb0072210.
• [13] Y. S. Pashkova, B.-Z. A. Rubshtein, M. A. Muratov, and G. Ya. Grabarnik, Foundations of symmetric spaces of measurable functions, Developments in Mathematics, vol. 45, Springer-Verlag 2016, DOI 10.1007/978-3-319-42758-4.
• [14] M. Pavlović, On the Banach envelope of Hardy-Orlicz spaces, Funct. Approx. Comment. Math. 20 (1992), 9-19.
• [15] M. M. Rao and Z. D. Ren, Theory of Orlicz spaces, Pure and Applied Mathematics, vol. 146, Marcel Dekker, Inc. 1991.
• [16] W. Rudin, Real and complex analysis, McGraw-Hill Book Company, New York 1987.
• [17] M. Rzeczkowski, On the Banach envelopes of Hardy-Orlicz spaces on an annulus, Ann. Pol. Math. 117 (2016), no. 2, 127-139, DOI 10.4064/ap3828-2-2016.
• [18] J. H. Shapiro, Mackey topologies, reproducing kernels and diagonal maps on the Hardy and Bergman spaces, Duke Math. J. 43 (1976), 187-202, DOI 10.1215/s0012-7094-76-04316-7.
• [19] A. L. Shields and D. L. Williams, Bounded projections, duality and multipliers in spaces of analytic functions, Trans. Amer. Math. Soc. 162 (1971), 287-305, DOI 10.2307/1995754.