A nonlinear functional on the Dirichlet space (Q1898954)

The nonlinear functional \(\Lambda_1(f)= (1/2\pi) \int^{2\pi}_0 e|f(e^{i\theta})|^2 d \theta\) was shown by Chang and Marshall to be bounded on the unit ball \(\mathfrak B\) of the space \(\mathfrak D\) of analytic functions in the unit disk with finite Dirichlet integral. The authors show that \(\Lambda_1\) is weakly continuous on \(\mathfrak B\) except at zero and that \(\Lambda_1\) attains its maximum over a subset of \(\mathfrak B\) determined by kernel functions.