Hankel operators in Schatten ideals

Abstract

We study membership to Schatten ideals S E , associated with a monotone RieszFischer space E, for the Hankel operators H f defined on the Hardy space H 2 (∂D). The conditions are expressed in terms of regularity of its symbol: we prove that H f ∈ S E if and only if f ∈ B E , the Besov space associated with a monotone Riesz-Fischer space E(dλ) over the measure space (D, dλ) and the main tool is the interpolation of operators.

Quantum Differentiability on Quantum Tori

“…Then by a result of V. Peller [42,Theorem 7.3], we have that for any p ∈ (0, ∞): df ∈ L p if and only if f is in the Besov space B 1/p p,p (T). Peller's work has been extended to obtain even more precise relationships between f and the singular values of df , for example L. Gheorghe [22] found necessary and sufficient conditions on f to ensure that df is in an arbitrary Riesz-Fisher space. For more details from a quantised calculus perspective, see [9, Chapter 4, Section 3.α].…”