Continuity and Schatten–von Neumann p-class membership of Hankel operators with anti-holomorphic symbols on (generalized) Fock spaces

AbstractIn this paper we investigate Hankel operators Hf¯:Am2→Am2⊥ with anti-holomorphic symbols f¯=∑k=0∞bkz¯k ∈L2(C,|z|m), where Am2 are general Fock spaces. We will show that Hf¯ is not continuous if the corresponding symbol is not a polynomial f¯=∑k=0Nbkz¯k. For polynomial symbols we will give necessary and sufficient conditions for continuity and compactness in terms of N and m. For monomials z¯k we will give a complete characterization of the Schatten–von Neumann p-class membership for p>0. Namely in case 2k<m the Hankel operators Hz¯k are in the Schatten–von Neumann p-class iff p>2m/(m−2k); and in case 2k⩾m they are not in the Schatten–von Neumann p-class