Weighted Banach spaces of harmonic functions

“The final publication is available at Springer via http://dx.doi.org/10.1007/s13398-012-0109-z."We study Banach spaces of harmonic functions on open sets of or endowed with weighted supremum norms. We investigate the harmonic associated weight defined naturally as the analogue of the holomorphic associated weight introduced by Bierstedt, Bonet, and Taskinen and we compare them. We study composition operators with holomorphic symbol between weighted Banach spaces of pluriharmonic functions characterizing the continuity, the compactness and the essential norm of composition operators among these spaces in terms of associated weights.The research of the first author was partially supported by MEC and FEDER Project MTM2010-15200 and by GV project ACOMP/2012/090.Jorda Mora, E.; Zarco García, AM. (2014). Weighted Banach spaces of harmonic functions. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas. 108(2):405-418. https://doi.org/10.1007/s13398-012-0109-zS4054181082Axler, S., Bourdon, P., Ramey, W.: Harmonic Function Theory, 2nd edn. Springer, Berlin (2001)Bierstedt, K.D., Bonet, J., Galbis, A.: Weighted spaces of holomorphic functions on balanced domains. Mich. Math. J. 40(2), 271–297 (1993)Bierstedt, K.D., Bonet, J., Taskinen, J.: Associated weights and spaces of holomorphic functions. Stud. Math. 127(2), 137–168 (1998)Bierstedt, K.D., Summers, W.H.: Biduals of weighted Banach spaces of analytic functions. J. Aust. Math. Soc. Ser. A 54(1), 70–79 (1993)Bonet, J., Domański, P., Lindström, M.: Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions. Can. Math. Bull. 42(2), 139–148 (1999)Bonet, J., Domański, P., Lindström, M.: Weakly compact composition operators on weighted vector-valued Banach spaces of analytic mappings. Ann. Acad. Sci. Fenn. Math. Ser. A I 26, 233–248 (2001)Bonet, J., Domański, P., Lindström, M., Taskinen, J.: Composition operators between weighted Banach spaces of analytic functions. J. Aust. Math. Soc. Ser. A 64, 101–118 (1998)Bonet, J., Friz, M., Jordá, E.: Composition operators between weighted inductive limits of spaces of holomorphic functions. Publ. Math. Debr. Ser. A 67, 333–348 (2005)Boyd, C., Rueda, P.: The v-boundary of weighted spaces of holomorphic functions. Ann. Acad. Sci. Fenn. Math. 30, 337–352 (2005)Boyd, C., Rueda, P.: Complete weights and v-peak points of spaces of weighted holomorphic functions. Isr. J. Math. 155, 57–80 (2006)Boyd, C., Rueda, P.: Isometries of weighted spaces of harmonic functions. Potential Anal. 29(1), 37–48 (2008)Carando, D., Sevilla-Peris, P.: Spectra of weighted algebras of holomorphic functions. Math. Z. 263, 887–902 (2009)Contreras, M.D., Hernández-Díaz, G.: Weighted composition operators in weighted Banach spaces of analytic functions. J. Aust. Math. Soc. Ser. A 69(1), 41–60 (2000)García, D., Maestre, M., Rueda, P.: Weighted spaces of holomorphic functions on Banach spaces. Stud. Math. 138(1), 1–24 (2000)García, D., Maestre, M., Sevilla-Peris, P.: Composition operators between weighted spaces of holomorphic functions on Banach spaces. Ann. Acad. Sci. Fenn. Math. 29, 81–98 (2004)Gunning, R., Rossi, H.: Analytic Functions of Several Complex Variables. AMS Chelsea Publishing, Providence (2009)Hoffman, K.: Banach Spaces of Analytic Functions. Prentice-Hall, Englewood Cliffs (1962)Krantz, S.G.: Function Theory of Several Complex Variables. AMS, Providence (2001)Lusky, W.: On weighted spaces of harmonic and holomorphic functions. J. Lond. Math. Soc. 51, 309–320 (1995)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Stud. Math. 175(1), 19–45 (2006)Meise, R., Vogt, D.: Introduction to Functional Analysis. Oxford University Press, Oxford (1997)Montes-Rodríguez, A.: Weight composition operators on weighted Banach spaces of analytic functions. J. Lond. Math. Soc. 61(2), 872–884 (2000)Ng, K.F.: On a theorem of Diximier. Math. Scand. 29, 279–280 (1972)Rudin, W.: Real and Complex Analysis. MacGraw-Hill, NY (1970)Rudin, W.: Functional analysis. In: International series in pure and applied mathematics, 2nd edn. McGraw-Hill, Inc., New York (1991)Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of harmonic functions. J. Reine Angew. Math. 299(300), 256–279 (1978)Shields, A.L., Williams, D.L.: Bounded projections and the growth of harmonic conjugates in the unit disc. Mich. Math. J. 29, 3–25 (1982)Zheng, L.: The essential norms and spectra of composition operators on $$H^\infty$$ . Pac. J. Math. 203(2), 503–510 (2002

The impact of viral mutations on recognition by SARS-CoV-2 specific T cells.

We identify amino acid variants within dominant SARS-CoV-2 T cell epitopes by interrogating global sequence data. Several variants within nucleocapsid and ORF3a epitopes have arisen independently in multiple lineages and result in loss of recognition by epitope-specific T cells assessed by IFN-γ and cytotoxic killing assays. Complete loss of T cell responsiveness was seen due to Q213K in the A∗01:01-restricted CD8+ ORF3a epitope FTSDYYQLY207-215; due to P13L, P13S, and P13T in the B∗27:05-restricted CD8+ nucleocapsid epitope QRNAPRITF9-17; and due to T362I and P365S in the A∗03:01/A∗11:01-restricted CD8+ nucleocapsid epitope KTFPPTEPK361-369. CD8+ T cell lines unable to recognize variant epitopes have diverse T cell receptor repertoires. These data demonstrate the potential for T cell evasion and highlight the need for ongoing surveillance for variants capable of escaping T cell as well as humoral immunity.This work is supported by the UK Medical Research Council (MRC); Chinese Academy of Medical Sciences(CAMS) Innovation Fund for Medical Sciences (CIFMS), China; National Institute for Health Research (NIHR)Oxford Biomedical Research Centre, and UK Researchand Innovation (UKRI)/NIHR through the UK Coro-navirus Immunology Consortium (UK-CIC). Sequencing of SARS-CoV-2 samples and collation of data wasundertaken by the COG-UK CONSORTIUM. COG-UK is supported by funding from the Medical ResearchCouncil (MRC) part of UK Research & Innovation (UKRI),the National Institute of Health Research (NIHR),and Genome Research Limited, operating as the Wellcome Sanger Institute. T.I.d.S. is supported by a Well-come Trust Intermediate Clinical Fellowship (110058/Z/15/Z). L.T. is supported by the Wellcome Trust(grant number 205228/Z/16/Z) and by theUniversity of Liverpool Centre for Excellence in Infectious DiseaseResearch (CEIDR). S.D. is funded by an NIHR GlobalResearch Professorship (NIHR300791). L.T. and S.C.M.are also supported by the U.S. Food and Drug Administration Medical Countermeasures Initiative contract75F40120C00085 and the National Institute for Health Research Health Protection Research Unit (HPRU) inEmerging and Zoonotic Infections (NIHR200907) at University of Liverpool inpartnership with Public HealthEngland (PHE), in collaboration with Liverpool School of Tropical Medicine and the University of Oxford.L.T. is based at the University of Liverpool. M.D.P. is funded by the NIHR Sheffield Biomedical ResearchCentre (BRC – IS-BRC-1215-20017). ISARIC4C is supported by the MRC (grant no MC_PC_19059). J.C.K.is a Wellcome Investigator (WT204969/Z/16/Z) and supported by NIHR Oxford Biomedical Research Centreand CIFMS. The views expressed are those of the authors and not necessarily those of the NIHR or MRC