A linear operator bounded in all Besov but not in Triebel-Lizorkin spaces

Key Points

• To construct a linear operator that is bounded in all Besov spaces but not in Triebel-Lizorkin spaces.
• Constructed a linear operator T using specific mathematical spaces.
• Analyzed the properties of Besov spaces and Triebel-Lizorkin spaces.
• Examined conditions under which T operates between these spaces.
• The operator T is shown to be bounded in Besov spaces B_{pq}^s.
• The operator T does not belong to Triebel-Lizorkin spaces F_{pq}^s, implying a significant distinction between the two.