In this paper, the commutative and spectral properties of a kth-order slant Hankel operator ( k ≥ 2, a fixed integer) on the Lebesgue space of n-dimensional torus, [Formula: see text], where [Formula: see text] is the unit circle, are studied. Characterizations for the commutativity and essential commutativity between higher order slant Hankel operators and slant Toeplitz operators have been obtained. The presence of an open disk in the point spectrum of a kth-order slant Hankel operator with a unimodular inducing function has also been ensured.
This paper focuses on the operator-theoretic properties (boundedness and
compactness) of Hankel operators on the Fock-Sobolev spaces Fp,m in terms of
symbols in BMO pr and VMO pr spaces, respectively, for a non-negative
integers m, 1 ? p < ? and r > 0. Along the way, we also study Berezin
transform of Hankel operators on Fp,m. 2020 Mathematics Subject
Classification. Primary 47B35; Secondary 30H20, 30H35. Keywords.
Fock-Sobolev spaces, Hankel operators, Berezin transform, BMO pr spaces, VMO
pr spaces.
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