Geodesic
$\mathrm{BMO}$-regularity for lattices of measurable functions on spaces of homogeneous type
Algebra i analiz, Tome 23 (2011) no. 2, pp. 248-295.

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D. V. Rutsky. $\mathrm{BMO}$-regularity for lattices of measurable functions on spaces of homogeneous type. Algebra i analiz, Tome 23 (2011) no. 2, pp. 248-295. http://geodesic.mathdoc.fr/item/AA_2011_23_2_a8/

[1] Kisliakov S. V., “Interpolation of $H_p$-spaces: some recent developments”, Function Spaces, Interpolation Spaces, and Related Topics (Haifa, 1995), Israel Math. Conf. Proc., 13, Bar-Ilan Univ., Ramat Gan, 1999, 102–140 | MR | Zbl

[2] Diening L., Hästö P., Nekvinda A., “Open problems in variable exponent Lebesgue and Sobolev spaces”, FSDONA 2004, Proceedings, eds. P. Drabek, J. Rakosnik, Milovy, Czech Republic, 2004, 38–58

[3] Kisliakov S. V., Xu Quan Hua, “Interpolation of weighted and vector-valued Hardy spaces”, Trans. Amer. Math. Soc., 343:1 (1994), 1–34 | DOI | MR | Zbl

[4] Kisliakov S. V., Xu Quan Hua, “Partial retractions for weighted Hardy spaces”, Studia Math., 138:3 (2000), 251–264 | MR | Zbl

[5] Cwikel M., McCarthy J. E., Wolff T. H., “Interpolation between weighted Hardy spaces”, Proc. Amer. Math. Soc., 116:2 (1992), 381–388 | DOI | MR

[6] Garnett J. B., Bounded analytic functions, Pure Appl. Math., 96, Acad. Press, New York–London, 1981 | MR | Zbl

[7] Stein E. M., Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Math. Ser., 43, Princeton Univ. Press, Princeton, NJ, 1993 | MR | Zbl

[8] Deng Donggao, Han Yongsheng, Harmonic analysis on spaces of homogeneous type, Lecture Notes in Math., 1966, Springer-Verlag, Berlin, 2009 | MR | Zbl

[9] Lindenstrauss J., Tzafriri L., Classical Banach spaces, v. I, Ergeb. Math. Grenzgeb., 92, Springer-Verlag, Berlin–New York, 1977 ; v. II, Ergeb. Math. Grenzgeb., 97, 1979 | MR | Zbl | MR | Zbl

[10] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, GITTL, M.–L., 1950

[11] Kislyakov S. V., “O BMO-regulyarnykh reshetkakh izmerimykh funktsii. II”, Zap. nauch. semin. POMI, 303, 2003, 161–168 | MR | Zbl

[12] Kislyakov S. V., “O BMO-regulyarnykh reshetkakh izmerimykh funktsii”, Algebra i analiz, 14:2 (2002), 117–135 | MR | Zbl

[13] Kislyakov S. V., “On BMO-regular couples of lattices of measurable functions”, Studia Math., 159:2 (2003), 277–290 | DOI | MR | Zbl

[14] Kislyakov S. V., “Bourgain analytic projection revisited”, Proc. Amer. Math. Soc., 126 (1998), 3307–3314 | DOI | MR | Zbl

[15] Mityagin B. S., “Interpolyatsionnaya teorema dlya modulyarnykh prostranstv”, Mat. sb., 66(108):4 (1965), 473–482 | MR | Zbl

[16] Bergh J., Löfström J., Interpolation spaces. An introduction, Grundlehren Math. Wiss., 223, Springer-Verlag, Berlin–New York, 1976 | MR | Zbl

[17] Hoffman K., Banach spaces of analytic functions, Prentice-Hall, Englewood Cliffs, NJ, 1962 | MR | Zbl

[18] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nevskii dialekt, Spb., 2004

[19] Rudin U., Teoriya funktsii v polikruge, Mir, M., 1974 | MR | Zbl

[20] Nikolskii N. K., Lektsii ob operatore sdviga, Nauka, M., 1980 | MR

[21] Diening L., Harjulehto P., Hästö P., Ruzicka M., Lebesgue and Sobolev spaces with variable exponents, a book manuscript in preparation, see http://www.helsinki.fi/~pharjule/varsob/publications.shtml

[22] Kalton N. J., “Complex interpolation of Hardy-type subspaces”, Math. Nachr., 171 (1995), 227–258 | DOI | MR | Zbl

[23] Fan Ky, “Fixed-point and minimax theorems in locally convex topological linear spaces”, Proc. Nat. Acad. Sci. U.S.A., 38 (1952), 121–126 | DOI | MR | Zbl

[24] Lozanovskii G. Ya., “O nekotorykh banakhovykh strukturakh”, Sib. mat. zh., 10 (1969), 584–599 | MR

[25] Rutskii D. V., “Dva zamechaniya o svyazi BMO-regulyarnosti i analiticheskoi ustoichivosti interpolyatsii dlya reshetok izmerimykh funktsii”, Zap. nauch. semin. POMI, 366, 2009, 102–115 | MR

[26] Rutskii D. V., “Zamechaniya o BMO-regulyarnosti i AK-ustoichivosti”, Zap. nauch. semin. POMI, 376, 2010, 116–166 | MR

[27] Benyamini Y., Sternfeld Y., “Spheres in infinite-dimensional normed spaces are Lipschitz contractible”, Proc. Amer. Math. Soc., 88:3 (1983), 439–445 | DOI | MR | Zbl

[28] Cruz-Uribe D., Fiorenza A., Martell J. M., Pérez C., “The boundedness of classical operators on variable $L^p$ spaces”, Ann. Acad. Sci. Fenn. Math., 31:1 (2006), 239–264 | MR

[29] Rubio de Francia J. L., “Factorization theory and $A_p$ weights”, Amer. J. Math., 106 (1984), 533–547 | DOI | MR | Zbl

[30] Hästö P., Diening L., Muckenhoupt weights in variable exponent spaces, Preprint, see , 2010 http://www.helsinki.fi/~pharjule/varsob/publications.shtml

[31] Kokilashvili V., Paatashvili V., “On variable Hardy and Smirnov classes of analytic functions”, Georgian Internat. J., 1:2 (2008), 181–195

[32] Gavrilov B. I., Subbotin A. V., “Maksimalnyi variant mnogomernoi teoremy Khinchina–Ostrovskogo i prilozheniya”, Dokl. RAN, 405:2 (2005), 158–160 | MR | Zbl

[33] Kopaliani T., “Interpolation theorems for variable exponent Lebesgue spaces”, J. Funct. Anal., 257:11 (2009), 3541–3551 | DOI | MR | Zbl

[34] Xu Quan Hua, “Some properties of the quotient space $L^1(\mathbb T^n)/H^1(\mathbb T^n)$”, Illinois J. Math., 37:3 (1993), 437–454 | MR | Zbl

[35] Xu Quan Hua, “Notes on interpolation of Hardy spaces”, Ann. Inst. Fourier (Grenoble), 42 (1992), 875–889 | MR | Zbl

[36] Anisimov D. S., Kislyakov S. V., “Dvoinye singulyarnye integraly: interpolyatsiya i ispravlenie”, Algebra i analiz, 16:5 (2004), 1–33 | MR | Zbl

[37] Kislyakov S. V., Shu Kuankhua, “Veschestvennaya interpolyatsiya i singulyarnye integraly”, Algebra i analiz, 8:4 (1996), 75–109 | MR | Zbl

[38] Lerner A. K., “Weighted norm inequalities for the local sharp maximal function”, J. Fourier Anal. Appl., 10:5 (2004), 465–474 | DOI | MR | Zbl

[39] Jawerth B., Torchinsky A., “Local sharp maximal functions”, J. Approx. Theory, 43 (1985), 231–270 | DOI | MR | Zbl

[40] Krivine J. L., Théorèmes de factorisation dans les espaces réticulés, Séminaire Maurey–Schwartz 1973–1974, Exp. No 22–23, Centre de Math., Ecole Polytech., Paris | MR | Zbl

[41] Dynkin E. M., Osilenker B. P., “Vesovye otsenki singulyarnykh integralov i ikh prilozheniya”, Itogi nauki i tekhn. Ser. mat. anal., 21, VINITI, M., 1983, 42–129 | MR | Zbl

[42] Hytönen T. P., The sharp weighted bound for general Calderón–Zygmund operators, Preprint, 2010, jul., arXiv: 1007.4330

[43] Orobitg J., Pérez C., “$A_p$ weights for nondoubling measures in $R^n$ and applications”, Trans. Amer. Math. Soc., 354 (2002), 2013–2033 | DOI | MR | Zbl

[44] Rubio de Francia J. L., “Linear operators in Banach lattices and weighted $L^2$-inequalities”, Math. Nachr., 133 (1987), 197–209 | DOI | MR | Zbl