| Title:
|
Weak and extra-weak type inequalities for the maximal operator and the Hilbert transform (English) |
| Author:
|
Gogatishvili, Amiran |
| Author:
|
Pick, Luboš |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
43 |
| Issue:
|
3 |
| Year:
|
1993 |
| Pages:
|
547-566 |
| . |
| Category:
|
math |
| . |
| MSC:
|
42B25 |
| MSC:
|
46E30 |
| MSC:
|
47B38 |
| MSC:
|
47G10 |
| idZBL:
|
Zbl 0798.42009 |
| idMR:
|
MR1249621 |
| DOI:
|
10.21136/CMJ.1993.128412 |
| . |
| Date available:
|
2009-09-24T09:33:14Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128412 |
| . |
| Reference:
|
[1] R.J. Bagby: Weak bounds for the maximal function in weighted Orlicz spaces.Studia Math. 95 (1990), 195–204. Zbl 0718.42018, MR 1060723, 10.4064/sm-95-3-195-204 |
| Reference:
|
[2] A. Carbery, S.-Y.A. Chang and J. Garnett: Weights and $L\log L$.Pacific J. Math. 120-1 (1985), 33–45. MR 0808927 |
| Reference:
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[3] R.R. Coifman: Distribution function inequalities for singular integrals.Proc. Nat. Acad. Sci. USA 69 (1972), 2838–2839. Zbl 0243.44006, MR 0303226, 10.1073/pnas.69.10.2838 |
| Reference:
|
[4] R.R. Coifman and C. Fefferman: Weighted norm inequalities for maximal functions and singular integrals.Studia Math. 51 (1974), 241–250. MR 0358205, 10.4064/sm-51-3-241-250 |
| Reference:
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[5] N. Fujii: Weighted bounded mean oscillation and singular integrals.Math. Japonica 22-5 (1978), 529–534. Zbl 0385.26010, MR 0481968 |
| Reference:
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[6] D. Gallardo: Weighted weak type integral inequalities for the Hardy-Littlewood maximal operator.Israel J. Math. 67-1 (1989), 95–108. Zbl 0683.42021, MR 1021364 |
| Reference:
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[7] J. García-Cuerva and J.L. Rubio de Francia: Weighted norm inequalities and related topics.North Holland, Amsterdam, 1985. MR 0807149 |
| Reference:
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[8] J.B. Garnett: Bounded analytic functions.Academic Press, New York-etc., 1981. Zbl 0469.30024, MR 0628971 |
| Reference:
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[9] A. Gogatishvili: Riesz transforms and maximal functions in $\phi (L)$ classes.Bull. Acad. Sci. Georgian SSR 137-3 (1990), 489–492. Zbl 0716.44004, MR 1087544 |
| Reference:
|
[10] A. Gogatishvili, V. Kokilashvili and M. Krbec: Maximal functions and $\phi (L)$ classes.Dokl. Akad. Nauk SSSR 314-3 (1990), 534–536. MR 1094013 |
| Reference:
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[11] S. Hruščev: A description of weights satisfying the $A_\infty $ condition of Muckenhoupt.Proc. Amer. Math. Soc. 90-2 (1984), 253–257. MR 0727244 |
| Reference:
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[12] R. A. Kerman and A. Torchinsky: Integral inequalities with weights for the Hardy maximal function.Studia Math. 71 (1982), 277–284. MR 0667316, 10.4064/sm-71-3-277-284 |
| Reference:
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[13] V. M. Kokilashvili: Maximal inequalities and multipliers in weighted Lizorkin-Triebel spaces.Soviet Math. Dokl. 19-2 (1978), 272–275. Zbl 0396.46034 |
| Reference:
|
[14] M. A. Krasnosel’skii and Ya. B. Rutitskii: Convex functions and Orlicz spaces.Noordhoff, Groningen, 1961. |
| Reference:
|
[15] M. Krbec: Two weights weak type inequalities for the maximal function in the Zygmund class.Function Spaces and Applications. Proc. Conf. Lund 1986, M. Cwikel et al. (eds.), Lecture Notes in Math. 1302, Springer, Berlin-etc., 1988, pp. 317–320. MR 0942276 |
| Reference:
|
[16] B. Muckenhoupt: Weighted norm inequalities for the Hardy maximal function.Trans. Amer. Math. Soc. 165 (1972), 207–227. Zbl 0236.26016, MR 0293384, 10.1090/S0002-9947-1972-0293384-6 |
| Reference:
|
[17] L. Pick: Two weights weak type inequality for the maximal function in $L(\log ^+L)^K$.Constructive Theory of Functions. Proc. Conf. Varna 1987, B. Sendov et al. (eds.), Publ. House Bulg. Acad. Sci., Sofia, 1988, pp. 377–381. MR 0994864 |
| Reference:
|
[18] L. Pick: Two-weight weak type maximal inequalities in Orlicz classes.Studia Math. 100-3 (1991), 207–218. Zbl 0752.42012, MR 1133385 |
| Reference:
|
[19] E. M. Stein: Singular integrals and the differentiability properties of functions.Academic Press, Princeton, 1970. MR 0290095 |
| . |
