Solid hulls and cores of weighted H-infinity-spaces

[EN] We determine the solid hull and solid core of weighted Banach spaces H-upsilon(infinity) of analytic functions functions f such that upsilon vertical bar f vertical bar is bounded, both in the case of the holomorphic functions on the disc and on the whole complex plane, for a very general class of radial weights upsilon. Precise results are presented for concrete weights on the disc that could not be treated before. It is also shown that if H-upsilon(infinity) is solid, then the monomials are an (unconditional) basis of the closure of the polynomials in H-upsilon(infinity). As a consequence H-upsilon(infinity) does not coincide with its solid hull and core in the case of the disc. An example shows that this does not hold for weighted spaces of entire functions.The research of Bonet was partially supported by the project MTM2016-76647-P. The research of Taskinen was partially supported by the Vaisala Foundation of the Finnish Academy of Sciences and Letters.Bonet Solves, JA.; Lusky, W.; Taskinen, J. (2018). Solid hulls and cores of weighted H-infinity-spaces. Revista Matemática Complutense. 31(3):781-804. https://doi.org/10.1007/s13163-018-0265-6781804313Anderson, J.M., Shields, A.L.: Coefficient multipliers of Bloch functions. Trans. Am. Math. Soc. 224, 255–265 (1976)Bennet, G., Stegenga, D.A., Timoney, R.M.: Coefficients of Bloch and Lipschitz functions. Ill. J. Math. 25, 520–531 (1981)Bierstedt, K.D., Bonet, J., Galbis, A.: Weighted spaces of holomorphic functions on bounded domains. Mich. Math. J. 40, 271–297 (1993)Bierstedt, K.D., Bonet, J., Taskinen, J.: Associated weights and spaces of holomorphic functions. Stud. Math. 127, 137–168 (1998)Blasco, O., Galbis, A.: On Taylor coefficients of entire functions integrable against exponential weights. Math. Nachr. 223, 5–21 (2001)Blasco, O., Pavlovic, M.: Coefficient multipliers on Banach spaces of analytic functions. Rev. Mat. Iberoam. 27, 415–447 (2011)Bonet, J., Taskinen, J.: Solid hulls of weighted Banach spaces of entire functions. Rev. Mat. Iberoam. 34, 593–608 (2018)Bonet, J., Taskinen, J.: Solid hulls of weighted Banach spaces of analytic functions on the unit disc with exponential weights. Ann. Acan. Sci. Fenn. Math. 43, 521–530 (2018)Constantin, O., Peláez, J.A.: Boundedness of the Bergman projection on $$L_p$$ L p -spaces with exponential weights. Bull. Sci. Math. 139(3), 245–268 (2015)Dostanić, M.R.: Multipliers in the space of analytic functions with exponential mean growth. Asymptot. Anal. 65(3–4), 191–201 (2009)Dostanić, M.-R.: Integration operators on Bergman spaces with exponential weight. Rev. Mat. Iberoam. 23(2), 421–436 (2007)Jevtić, M., Pavlović, M.: On the solid hull of the Hardy-Lorentz space. Publ. Inst. Math. (Beogr.) (N.S.) 85(99), 55–61 (2009)Jevtić, M., Vukotić, D., Arsenović, M.: Taylor Coefficients and Coefficient Multipliers of Hardy and Bergman-Type Spaces. RSME Springer Series, vol. 2. Springer, Berlin (2016)Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces I. Springer, Berlin (1977)Lusky, W.: On the Fourier series of unbounded harmonic functions. J. Lond. Math. Soc. 2(61), 568–580 (2000)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Stud. Math. 175, 19–45 (2006)Pau, J., Peláez, J.A.: Volterra type operators on Bergman spaces with exponential weights. Contemp. Math. 561, 239–252. Topics in complex analysis and operator theory. American Mathematical Society, Providence (2012)Pavlović, M.: On harmonic conjugates with exponential mean growth. Czech. Math. J. 49, 733–742 (1999)Pavlović, M.: Function Classes on the Unit Disc: An Introduction. De Gruyter Studies in Mathematics, vol. 52, p. 449. De Gruyter, Berlin (2014)Peláez, J.A., Rättyä, J.: Weighted Bergman Spaces Induced by Rapidly Increasing Weights, vol. 227, no. 1066, pp. vi+124. American Mathematical Society (2014)Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of analytic functions. Trans. Am. Math. Soc. 162, 287–302 (1971