Resumen de Hadamard gap series in growth spaces

Kjersti Solberg Eikrem

• Let ℎ∞? be the class of harmonic functions in the unit disk which admit a two-sided radial majorant v(r). We consider functions v that fulfill a doubling condition. We characterize functions in ℎ∞? that are represented by Hadamard gap series in terms of their coefficients, and as a corollary we obtain a characterization of Hadamard gap series in Bloch-type spaces for weights with a doubling property. We show that if ?∈ℎ∞? is represented by a Hadamard gap series, then u will grow slower than v or oscillate along almost all radii. We use the law of the iterated logarithm for trigonometric series to find an upper bound on the growth of a weighted average of the function u, and we show that the estimate is sharp.