Carleson’s formula for some weighted Dirichlet spaces

[1] A. Aleman, Hilbert spaces of analytic functions between the Hardy and the Dirichlet space, Proc. Amer. Math. Soc 115 (1992), 97–104. Search in Google Scholar

[2] N. Arcozzi, R. Rochberg, E.T. Sawyer, and B.D. Wick, The Dirichlet space: a survey, New York J. Math. 17A (2011), 45–86, Search in Google Scholar

[3] A. Beurling, Ensembles exceptionnels, Acta Math. 72 (1939), 1–13. Search in Google Scholar

[4] B. Böe, A norm on the holomorphic Besov space, Proc. Amer. Math. Soc. 131 (2003), 235–241 Search in Google Scholar

[5] L. Carleson, A representation formula for the Dirichlet integral, Math. Z. 73 (1960) 190–196. Search in Google Scholar

[6] A. Devinatz and I. I. Hirschman, Multiplier transformations on l²,^α, Ann. Math. 69, No. 3 (1959), 575–587. Search in Google Scholar

[7] J. Douglas, Solution of the problem of Plateau, Trans. Amer. Math. Soc. 33 (1931), no. 1, 263–321. Search in Google Scholar

[8] K. M. Dyakonov, Besov spaces and outer functions, Michigan Math. J. 45 (1998), no. 1, 143–157. Search in Google Scholar

[9] O. El-Fallah, K. Kellay, J. Mashreghi and T. Ransford, A primer on the Dirichlet space, Cambridge Tracts in Mathematics, 203. Cambridge University Press, Cambridge, 2014. xiv+211 pp. Search in Google Scholar

[10] J. Garnett, Bounded Analytic Functions, Springer, New York, 2007. Search in Google Scholar

[11] S. Richter, A representation theorem for cyclic analytic two-isometries, Trans. Amer. Math. Soc., 328 (1991) 325–349. Search in Google Scholar

[12] S. Richter and C. Sundberg, A formula for the local Dirichlet integral, Michigan Math. J. 38 (1991) 355–379. Search in Google Scholar

[13] W. T. Ross, The classical Dirichlet space. Recent advances in operator-related function theory, 171–197, Contemp. Math., 393, Amer. Math. Soc., Providence, RI, 2006. Search in Google Scholar

[14] N. A. Shirokov, Outer functions in O.V. Besov’s analytic classes, Journal of Math. Sci. 85 (1997), no. 2, 1867–1897. Search in Google Scholar

[15] N. A. Shirokov, Ideals and factorization in algebras of analytic functions that are smouth up to the boundary, Trudy Mat. Inst. Steklov. 130 (1978), 196–222; English transl. in Proc. Steklov Inst. Math. 130 (1979), 205–233. Search in Google Scholar

[16] S. A. Vinogradov and N. A. Shirokov Factorization of analytic functions having a derivative in H^p, Journal of Soviet Mathematics March–April, 1974, Volume 2, Issue 2, pp 68–83. Search in Google Scholar