Constructed a linear operator showing it is bounded in Besov spaces but not in Triebel-Lizorkin spaces, indicating key differences in space properties.
We construct a linear operator T : S ′ ( R n ) → S ′ ( R n ) T: S’( R^n)→ S’( R^n) such that T : B p q s ( R n ) → B p q s ( R n ) T: Bpq^s( R^n)→ Bpq^s( R^n) for all 0 > p , q ≤ ∞ 0>p,q≤ ∞ and s ∈ R s∈ R , but T ( F p q s ( R n ) ) ⊄ F p q s ( <mml:ms
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Liding Yao (2026) studied this question.
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