For each p > 0 we provide the construction of a harmonic function on a homogeneous isotropic tree T in the Bergman space A(p) (sigma) with no finite radial limits anywhere. Here, sigma is an analogue of the Lebesgue measure on the tree. With the appropriate modifications, the construction yields a function in A(1) (sigma) when T is a rooted radial tree such that the number of forward neighbors increases so slowly that their reciprocals are not summable.
Cohen, J., Colonna, F., Picardello, A., Singman, D. (2018). Fractal functions with no radial limits in Bergman spaces on trees. HOKKAIDO MATHEMATICAL JOURNAL, 47(2), 269-289.
Fractal functions with no radial limits in Bergman spaces on trees
Picardello, AM;
2018-01-01
Abstract
For each p > 0 we provide the construction of a harmonic function on a homogeneous isotropic tree T in the Bergman space A(p) (sigma) with no finite radial limits anywhere. Here, sigma is an analogue of the Lebesgue measure on the tree. With the appropriate modifications, the construction yields a function in A(1) (sigma) when T is a rooted radial tree such that the number of forward neighbors increases so slowly that their reciprocals are not summable.File in questo prodotto:
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