Compact Hankel operators with conjugate analytic symbols (Q1275729)

The author characterize conjugate analytic symbols \(f\) of compact Hankel operators \(H_f\) acting on the Bergman spaces \(L^p_a\), \(1\leq p<\infty\) of the unit disk. The author first considers the case \(1<p<\infty\) and proves the following: For the conjugate analytic symbol \(f\), the Hankel operator \(H_f:L^p_a \to L^p\) is compact if and only if \(f\) is in the little Bloch space. This is a generalization of the result for the case \(p=2\) given by \textit{S. Axler} [Duke. Math. J. 53, 315-332 (1986; Zbl 0633.47014)]. The author also considers the case \(p=1\) and proves the following: For the conjugate analytic symbol \(f\), the Hankel operator \(H_f:L^1_a \to L^1\) is *-compact if and only if \[ (1-|z|^2)|f'(z)|\log\frac{1}{1-|z|^2} \to 0 \qquad(|z|\to 1). . \]