Discrete analogue of generalized Hardy spaces and multiplication operators on homogenous trees

Aleman, A., Duren, P.L., Martin, M.J., Vukotić, D.: Multiplicative isometries and isometric zero-divisors. Canad. J. Math. 62, 961–974 (2010)

Allen, R.F., Colonna, F., Easley, G.R.: Multiplication operators between Lipschitz-type spaces on a tree. Int. J. Math. Math. Sci. Art. ID 472495. 36 (2011)

Allen, R.F., Colonna, F., Easley, G.R.: Multiplication operators on the iterated logarithmic Lipschitz spaces of a tree. Mediterr. J. Math. 9, 575–600 (2012)

Allen, R.F., Colonna, F., Easley, G.R.: Multiplication operators on the weighted Lipschitz space of a tree. J. Oper. Theor. 69, 209–231 (2013)

Allen, R.F., Colonna, F., Easley, G.R.: Composition operators on the Lipschitz space of a tree. Mediterr. J. Math. 11, 97–108 (2014)

Biase, F.D., Picardello, M.A.: The Green formula and $$H^p$$ H p spaces on trees. Math. Z. 218, 253–272 (1995)

Campbell, D.M., Leach, R.J.: A survey of $$H^p$$ H p multipliers as related to classical function theory. Complex Variab. Theor. Appl. 3, 85–111 (1984)

Chen, Sh, Ponnusamy, S., Rasila, A.: On characterizations of Bloch-type, Hardy-type and Lipschitz-type spaces. Math. Z. 279, 163–183 (2015)

Clunie, J.G., Anderson, J.M., Pommerenke, Ch.: On Bloch functions and normal functions. J. Reine Angew. Math. 270, 12–37 (1974)

Colonna, F., Easley, G.R.: Multiplication operators on the Lipschitz space of a tree. Integr. Equ. Oper. Theory 68, 391–411 (2010)

Colonna, F., Easley, G.R.: Multiplication operators between the Lipschitz space and the space of bounded functions on a tree. Mediterr. J. Math. 9, 423–438 (2012)

Conway, J.B.: A course in functional analysis, 2nd edn. Springer, New York (1990)

Diestel, R.: Graph Theory, 4th edn. Springer, New York (2010)

Duren, P.L., Romberg, B.W., Shields, A.L.: Linear functionals on $$H^p$$ H p spaces with $$0<p<1$$ 0 < p < 1 . J. Reine Angew. Math. 238, 32–60 (1969)

Duren, P.L.: Theory of $$H^p$$ H p Spaces. Academic Press, New York and London (1970)

El-Fallah, O., Kellay, K., Mashreghi, J., Ransford, T.: A primer on the Dirichlet space. Cambridge University Press, Cambridge (2014)

Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces. Springer-Verlag, New York (2000)

Korányi, A., Picardello, M.A., Taibleson, M.H.: Hardy spaces on non-homogeneous trees. Symp. Math. 29, 205–265 (1987)

Manhas, J.S.: Composition operators and multiplication operators on weighted spaces of analytic functions. Int. J. Math. Math. Sci. Art. ID 92070. 21 (2007)

Pavlović, M.: Function Classes on the Unit Disc. An introduction. De Gruyter Studies in Mathematics, pp. 52. De Gruyter, Berlin (2014)

Rudin, W.: Functional analysis, $$2$$ 2 nd edn.In: International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York (1991)

Shapiro, J.H.: Composition Operators and Classical Function Theory. Springer, New York (1993)

Vukotić, D.: Analytic Toeplitz operators on the Hardy space $$H^p$$ H p : a survey. Bull. Belg. Math. Soc. 10, 101–113 (2003)

Zhu, K.: Operator Theory in Function Spaces. Marcel Dekker, New York (1990)