Schatten Class Membership of Hankel Operators on the Unit Sphere
نویسندگان
چکیده
Let H(S) be the Hardy space on the unit sphere S in C, n ≥ 2. Consider the Hankel operator Hf = (1 − P )Mf |H(S), where the symbol function f is allowed to be arbitrary in L(S, dσ). We show that for p > 2n, Hf is in the Schatten class Cp if and only if f − Pf belongs to the Besov space Bp. To be more precise, the “if” part of this statement is easy. The main result of the paper is the “only if ” part. We also show that the membership Hf ∈ C2n implies f − Pf = 0, i.e., Hf = 0.
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