## (Weak) compactness of Hankel operators on $$BMOA$$.(English)Zbl 1303.47042

Let $$H^p=H^p(\mathbf T)$$, $$1\leq p<\infty$$, be the Hardy space over the unit circle $$\mathbf T$$ which consists of all functions $$f$$ in $$L^p=L^p(\mathbf T)$$ such that the Fourier coefficients $$\hat f(n)$$ all vanish for $$n<0$$. Let $$BMOA$$ be the dual of $$H^1$$, which is identified with $$BMO\cap H^1$$, where $$BMO=BMO(\mathbf T)$$ is the standard space of functions with bounded mean oscillations over $$\mathbf T$$. For $$a\in H^2$$ with $$\hat a(0)=0$$, the Hankel operator $$H_a$$ with symbol $$a$$ is defined by $$H_a(f)=P(a Jf)$$, where $$Jf(\zeta)=\overline{\zeta}f(\overline{\zeta})$$ and $$P: L^2 \to H^2$$ is the Hilbert space orthogonal projection, i.e., the Riesz projection.
When $$H_a$$ is bounded on $$BMOA$$, the author obtains several equivalent conditions for the (weak) compactness of $$H_a$$ on $$BMOA$$. In particular, it is shown that the compactness and the weak compactness of $$H_a$$ on $$BMOA$$ are the same.

### MSC:

 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 30H35 BMO-spaces 30H10 Hardy spaces
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