Weak and extra-weak type inequalities for the maximal operator and the Hilbert transform
Czechoslovak Mathematical Journal, Tome 43 (1993) no. 3, pp. 547-566
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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DOI : 10.21136/CMJ.1993.128412
Classification : 42B25, 46E30, 47B38, 47G10
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Gogatishvili, Amiran; Pick, Luboš. Weak and extra-weak type inequalities for the maximal operator and the Hilbert transform. Czechoslovak Mathematical Journal, Tome 43 (1993) no. 3, pp. 547-566. doi: 10.21136/CMJ.1993.128412

[1] R.J. Bagby: Weak bounds for the maximal function in weighted Orlicz spaces. Studia Math. 95 (1990), 195–204. | DOI | MR | Zbl

[2] A. Carbery, S.-Y.A. Chang and J. Garnett: Weights and $L\log L$. Pacific J. Math. 120-1 (1985), 33–45. | MR

[3] R.R. Coifman: Distribution function inequalities for singular integrals. Proc. Nat. Acad. Sci. USA 69 (1972), 2838–2839. | DOI | MR | Zbl

[4] R.R. Coifman and C. Fefferman: Weighted norm inequalities for maximal functions and singular integrals. Studia Math. 51 (1974), 241–250. | DOI | MR

[5] N. Fujii: Weighted bounded mean oscillation and singular integrals. Math. Japonica 22-5 (1978), 529–534. | MR | Zbl

[6] D. Gallardo: Weighted weak type integral inequalities for the Hardy-Littlewood maximal operator. Israel J. Math. 67-1 (1989), 95–108. | MR | Zbl

[7] J. García-Cuerva and J.L. Rubio de Francia: Weighted norm inequalities and related topics. North Holland, Amsterdam, 1985. | MR

[8] J.B. Garnett: Bounded analytic functions. Academic Press, New York-etc., 1981. | MR | Zbl

[9] A. Gogatishvili: Riesz transforms and maximal functions in $\phi (L)$ classes. Bull. Acad. Sci. Georgian SSR 137-3 (1990), 489–492. | MR | Zbl

[10] A. Gogatishvili, V. Kokilashvili and M. Krbec: Maximal functions and $\phi (L)$ classes. Dokl. Akad. Nauk SSSR 314-3 (1990), 534–536. | MR

[11] S. Hruščev: A description of weights satisfying the $A_\infty $ condition of Muckenhoupt. Proc. Amer. Math. Soc. 90-2 (1984), 253–257. | MR

[12] R. A. Kerman and A. Torchinsky: Integral inequalities with weights for the Hardy maximal function. Studia Math. 71 (1982), 277–284. | DOI | MR

[13] V. M. Kokilashvili: Maximal inequalities and multipliers in weighted Lizorkin-Triebel spaces. Soviet Math. Dokl. 19-2 (1978), 272–275. | Zbl

[14] M. A. Krasnosel’skii and Ya. B. Rutitskii: Convex functions and Orlicz spaces. Noordhoff, Groningen, 1961.

[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

[16] B. Muckenhoupt: Weighted norm inequalities for the Hardy maximal function. Trans. Amer. Math. Soc. 165 (1972), 207–227. | DOI | MR | Zbl

[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

[18] L. Pick: Two-weight weak type maximal inequalities in Orlicz classes. Studia Math. 100-3 (1991), 207–218. | MR | Zbl

[19] E. M. Stein: Singular integrals and the differentiability properties of functions. Academic Press, Princeton, 1970. | MR

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