Positive Toeplitz Operators from aWeighted Harmonic Bloch Space into Another

Abstract

In the present paper, we define positive general Toeplitz operators between weighted harmonic Bloch spaces 𝑏∞𝛼 on the unit ball of R𝑛 for the full range of parameter 𝛼 ∈ R, where symbols are positive Borel measures on the unit ball of R𝑛. We characterize the boundedness and compactness of Toeplitz operators from one weighted harmonic Bloch space into another in terms of Carleson measures and vanishing Carleson measures. Recently, in Doğan (2022), positive symbols of bounded and compact general Toeplitz operators between harmonic Bergman-Besov spaces are completely characterized in term of Carleson measures and vanishing Carleson measures. Our results extend those known for harmonic Bloch space.

Keywords

• toeplitz operator
• harmonic Bergman-Besov space
• weighted harmonic Bloch space
• carleson measure

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