BMO-type characterizations and the diagonal mapping and boundedness of integral operators in some spaces of analytic functions

R. F. Shamoyan

Vladikavkazskij matematičeskij žurnal, Tome 9 (2007) no. 2, pp. 40-53

Bibliographie

[1] Holland F., Walsh D., “Criteria for membership of Bloch spaces and it is subspace BMOA”, Math. Ann., 273 (1986), 317–335 | DOI | MR | Zbl

[2] Stroethoff K., “The Bloch spaces and Besov spaces of analitic functions”, Bull Austr. Math. Soc., 54 (1996), 211–219 | DOI | MR | Zbl

[3] Pekarskii A. A., “Novoe dokazatelstvo neravenstva Semmesa dlya proizvodnoi ratsionalnoi funktsii”, Mat. zametki, 72:2 (2002), 258–264 | MR | Zbl

[4] Aleman A., Cima J., “An integral operator on $H^p$ and Hardy's enequality”, J. D'Analise Math., 85 (2001), 157–175 | DOI | MR

[5] Duren P. L., Theory of $H^p$-spaces, Acad. Press, N-Y–London, 1970 | MR | Zbl

[6] Alexandrov A. B., “Essays on non Locally convex Hardy classes”, Lecture Notes in Math., 864, 1981, 1–90

[7] Shamoyan R. F., “Obobschennoe preobrazovanie Khardi i operatory Teplitsa v prostranstvakh tipa VMOA”, Ukr. mat. zhurn., 9:53 (2001), 1206–1271 | MR

[8] Djrbashian, Shamoyan F., Topics in the theory of $A^p_{\alpha}$ spaces, Teubner Texte zur Math., 105, 1988, 199 pp. | MR | Zbl

[9] Boe B., “Interpolating sequences for Besov spaces”, J. of Func. Anal., 192 (2001), 319–341 | DOI | MR

[10] Wu Z., “The Predual and second Predual of $\omega_{\alpha}$”, J. of Func. Anal., 116 (1993), 314–334 | DOI | MR | Zbl

[11] Shamoyan R. F., “O kharakteristikakh tipa VMO odnogo klassa golomorfnykh v kruge funktsii”, Sib. mat. zhurn., 44:3 (2003), 539–560 | MR | Zbl

[12] Aleman A., Siskakis A. G., “Integration operators on Bergman spaces”, Indiana Un. M. J., 46:2 (1997), 337–356 | MR | Zbl

[13] Aleman A., Siskakis A. G., “An integral operator on $H^p$”, Complex Variables, 28:11 (1995), 149–158 | MR | Zbl

[14] Shamoyan F. A., Yaroslavtseva O. V., “Nepreryvnye proektory, dvoistvennost diagonalnoe otobrazhenie v vesovykh prostranstvakh golomorfnykh funktsii so smeshannoi normoi”, Zap. sem. POMI, 225, 1998, 184–197

[15] Tribel Kh., Teoriya funktsionalnykh prostranstv, Mir, M., 1983, 344 pp. | MR

[16] Ortega J., Fabrega J., “Corona type decomposition in some Besov spaces”, Math. Scand., 78:1 (1996), 93–111 | MR | Zbl

[17] Nakazi T., Canad Nath Bull., 39:2 (1996), 219–226 | MR | Zbl

[18] Dynkin E., “Rational Function in Bergman spaces”, Complex analisys, operators and related topics, Oper. Adv. Appl., 113, 2000, 77–94 | MR

[19] Ortega J. M., Fabrega J., “Holomorphic Triebel-Lizorkin spaces”, J. of Func. Anal., 151 (1998), 177–212 | DOI | MR

[20] Cohn W., Verbitski I., “Factorization on tent spaces and Hankel operators”, J. of Func. Anal., 175 (2000), 308–329 | DOI | MR | Zbl

[21] Wu Z., Xie C., “$Q_p$ spaces and Morrey spaces”, J. of Func. Anal., 164 (2003), 1–15

[22] Shamoyan R. F., “O deistvii operatorov svertki i Teplitsa v prostranstvakh tipa VMOA”, Mat. zametki, 73:5 (2003), 759–772 | MR

[23] Dyakonov K., Girela D., “On $Q_p$ spaces and pseudoanalityc extention”, Ann. Acad. Sci. Fenn., 25 (2000), 477–487 | MR

[24] Essen M., Xiao, “Some results on $Q_p$ spaces $0

1$”, J. Reinge. Angew. Math., 485 (1997), 173–195 | MR | Zbl

[25] Bonami A., Bekolle D., “Inegalites a poids pour le noyay de Bergman”, C. R. Acad. Sci. Paris Ser. A, 286:18 (1978) | MR | Zbl

[26] Khavin V., “On the factorization of analytic functions smooth up to the boundary”, Zap. Nauchn. Sem. LOMI, 22, 1971, 202–205 | MR | Zbl

[27] Essen M., Wulan H., “On analytic and meromorphic function and spaces of $Q_p$ type”, J. Math., 46:4 (2002), 1233–1258 | MR | Zbl

[28] Shamoyan R. F., “O prostranstvakh golomorfnykh v polikruge funktsii tipa Lizorkina — Tribelya”, Izvestiya NAN Arm., 37:3 (2002), 57–78 | MR | Zbl