Geodesic
Interpolation of abstract spaces of Hardy type
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 49, Tome 503 (2021), pp. 22-56 Cet article a éte moissonné depuis la source Math-Net.Ru

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Interpolation theorems are proved for Hardy-type spaces arising form certain uniform algebras more general than weak*-Dirichlet algebras. It is shown that, in a sense, the entire setting is not sensitive to the introduction of a weight. Some generalizations that model the case of two variables are also discussed. 
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V. A. Borovitskiy; S. V. Kislyakov. Interpolation of abstract spaces of Hardy type. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 49, Tome 503 (2021), pp. 22-56. http://geodesic.mathdoc.fr/item/ZNSL_2021_503_a1/

[1] T. W. Gamelin, S. V. Kislyakov, “Uniform algebras as Banach spaces”, Handbook of the geometry of Banach spaces, v. 1, 2001, 671–706 | DOI | MR | Zbl

[2] S. V. Kisliakov,, “Interpolation of $H^p$-spaces: some recent developments”, Israel Math. Conf. Proceedings, 13 (1999), 102–140 | MR | Zbl

[3] S. V. Kisliakov, “Bourgain's analytic projection revisited”, Proceed. Amer. Math. Soc., 126:11 (1998), 3307–3314. | DOI | Zbl

[4] S. V. Kisliakov, I. K. Zlotnikov, “Interpolation for intersections of Hardy-type spaces”, Israel J. Math, 239 (2020), 21–38 | DOI | MR | Zbl

[5] S. V. Kisliakov, “Interpolation involving bounded bianalytic functions”, Complex Analysis, Operators, and Related Topics, 2000, 135–149 | DOI | Zbl

[6] G. Pisier, “Interpolation between $H^p$ spaces and noncommutative generalizations. I”, Pacific J. Math., 155:2 (1992), 341–368 | DOI | MR | Zbl

[7] T. P. Srinivasan, J.-K. Wang, “Weak*-Dirichlet algebras, Function Algebras”, Funct. Algebras, Proc. Internat. Sympos. (Tulane Univ., 1965), Scott-Foresman, Chicago, IL, 1966, 216–249

[8] E. Stein, T. S. Murphy, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton University Press, 1993 | Zbl

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

[10] V. A. Borovitskii, “$K$-zamknutost dlya vesovykh prostranstv Khardi na tore $\mathbb{T}^2$”, Zap. nauchn. semin. POMI, 456, 2017, 25–36

[11] I. K. Zlotnikov, S. V. Kislyakov, “Teorema Grotendika dlya nekotorykh algebr i modulei nad nimi”, Zap. nauchn. semin. POMI, 480, 2019, 108–121

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