| Title:
|
On Besov-Hardy-Sobolev spaces of analytic functions in the unit disc (English) |
| Author:
|
Oswald, P. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
33 |
| Issue:
|
3 |
| Year:
|
1983 |
| Pages:
|
408-426 |
| . |
| Category:
|
math |
| . |
| MSC:
|
30D55 |
| MSC:
|
42A10 |
| MSC:
|
46E35 |
| idZBL:
|
Zbl 0594.46027 |
| idMR:
|
MR718924 |
| DOI:
|
10.21136/CMJ.1983.101891 |
| . |
| Date available:
|
2008-06-09T14:55:25Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101891 |
| . |
| Reference:
|
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| Reference:
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[2] С. Fefferman E. M. Stein: Some maximal inequalities.Amer. J. Math., 93 (1971), 107- 115. MR 0284802, 10.2307/2373450 |
| Reference:
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[3] С. Fefferman E. M. Stein: $H^p$ spaces of several variables.Acta Math., 129 (1972), 136- 193. MR 0447953 |
| Reference:
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[4] T. M. Flett: On an extension of absolute summability and some theorems of Littlewood and Paley.Proc. Lond. Math. Soc., 7 (1957), 113-141. Zbl 0109.04402, MR 0086912, 10.1112/plms/s3-7.1.113 |
| Reference:
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[5] T. M. Flett: Mean values of power series.Рас. J. Math., 25 (1968), 463 - 494. Zbl 0162.10002, MR 0229807 |
| Reference:
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[6] T. M. Flett: Lipschitz spaces of functions on the circle and the disc.J. Math. Anal. Appl., 39 (1972), 125-158. Zbl 0253.46084, MR 0313779, 10.1016/0022-247X(72)90230-2 |
| Reference:
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[7] V. I. Ivanov: Direct and inverse theorems of approximation theory in the metric $L_p$ for $0 < p < 1$.Mat. Zametki, 18 (1975), 641 - 658 (in Russian). MR 0412710 |
| Reference:
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[8] S. M. Nikolskij: Approximation of functions of several variables and imbedding theorems.Nauka, Moskva, 1977 (in Russian). MR 0506247 |
| Reference:
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[9] P. Oswald: Approximation by splines in the metric $L_p$, $0 < p < 1$.Math. Nachr., 94 (1980), 69-96 (in Russian). MR 0582521 |
| Reference:
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[10] J. Peetre: New thoughts on Besov spaces.Duke Univ. Math. Ser., Durham, 1976. Zbl 0356.46038, MR 0461123 |
| Reference:
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[11] J. L. Rubio de Francia: Vector valued inequalities for Fourier series.Proc. Amer. Math. Soc., 78 (1980), 525-528. MR 0556625 |
| Reference:
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[12] H.-J. Schmeisser W. Sickel: On strong summability of multiple Fourier series and smoothness properties of functions.Anal. Math., 8 (1982), 57-70. MR 0662704, 10.1007/BF02073772 |
| Reference:
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[13] E. M. Stein: A maximal function with applications to Fourier series.Ann. Math., 68 (1958), 584-603. Zbl 0085.05602, MR 0100197, 10.2307/1970157 |
| Reference:
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[14] E. M. Stein: Singular integrals and differentiability properties of functions.Princ. Univ. Press, Princeton, 1970. Zbl 0207.13501, MR 0290095 |
| Reference:
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[15] E. M. Stein G. Weiss: Introduction to Fourier analysis in Euclidean spaces.Princ. Univ. Press, Princeton, 1971. MR 0304972 |
| Reference:
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[16] E. A. Storoženko: Approximation of functions of the class $H^p$, $0 < p < 1$.Mat. Sbornik, 105 (147) (1978), 601-621 (in Russian). MR 0496597 |
| Reference:
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[17] E. A. Storoženko: On theorems of Jackson type for $H^p$, $0 < p < 1$.Izv. Akad. Nauk SSSR, Ser. mat., 44 (1980), 948-962 (in Russian). MR 0587344 |
| Reference:
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[18] E. A. Storoženko V. G. Krotov P. Oswald: Direct and inverse theorems of Jackson type in the spaces $L_p$, $0 < p < 1$.Mat. Sbornik, 98 (140) (1975), 395-415 (in Russian). MR 0402384 |
| Reference:
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[19] M. H. Taibleson: On the theory of Lipschitz spaces of distributions on Euclidean $n$-space I, II.J. Math. Mech., 13 (1964), 407-479; 14 (1965), 821-839. |
| Reference:
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[20] W. Trebels: Multipliers for $(C, \alpha)$-bounded Fourier expansions in Banach spaces and approximation theory.Lect. Notes Math., 329, Springer, Berlin-Heidelberg-New York, 1973. MR 0510852, 10.1007/BFb0060959 |
| Reference:
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[21] H. Triebel: Interpolation theory, function spaces, differential operators.Deut. Verl. Wiss., Berlin, 1978. Zbl 0387.46033, MR 0500580 |
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| Reference:
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[23] H. Triebel: Spaces of Besov-Hardy-Sobolev type.Teubner-Texte Math., Teubner, Leipzig, 1978. Zbl 0408.46024, MR 0581907 |
| Reference:
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[24] H. Triebel: Periodic spaces of Besov-Hardy-Sobolev type and related maximal functions for trigonometrical polynomials.Forschungsergebnisse FSU Jena, N/80/11, 1980. |
| Reference:
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[25] A. Zygmund: Trigonometric series.vol. 1, 2, Cambr. Univ. Press, Cambridge, 1959. Zbl 0085.05601, MR 0107776 |
| . |
