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Let $\mathcal{H}(\mathbb{D})$ be the space of analytic functions on the unit disc $\mathbb{D}$. Let $\psi=(\psi_j)_{j=0}^n$ and $\Phi=(\Phi_j)_{j=0}^n$ be such that $\psi_j, \Phi_j \in \mathcal{H}(\mathbb{D})$. The linear differential operator is defined by $ T_{\psi}(f)=\sum_{j=0}^n \psi_j f^{(j)},$ $f\in \mathcal{H}(\mathbb{D})$. We characterize the boundedness and compactness of the difference operator $ (T_{\psi}-T_{\Phi})(f)=\sum_{j=0}^n \left(\psi_j-\Phi_j\right) f^{(j)}$ between weighted-type spaces of analytic functions. As applications, we obtained boundedness and compactness of the difference of multiplication operators between weighted-type and Bloch-type spaces. Also, we give examples of unbounded (non compact) differential operators such that their difference is bounded (compact).
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참고문헌 (31)
참고문헌 신청
Earl Berkson / 1981 / Composition Operators Isolated in the Uniform Operator Topology / Proceedings of the American Mathematical Society 81(2):230~232
K. D. Bierstedt / 1993 / Weighted spaces of holomorphic functions on balanced domains / Michigan Math. J 40(2,):271~297
K. D. Bierstedt / 1998 / Associated weights and spaces of holomorphic functions / Studia Math 127(2):137~168
K. D. Bierstedt / 1993 / Biduals of weighted Banach spaces of analytic functions / J. Austral. Math. Soc. Ser. A 54(1):70~79
J. Bonet / 1998 / Composition operators between weighted Banach spaces of analytic functions / ustral. Math. Soc. Ser. A 64(1):101~118
K. D. Bierstedt / 1993 / Weighted spaces of holomorphic functions on balanced domains / Michigan Math. J 40(2,):271~297
K. D. Bierstedt / 1998 / Associated weights and spaces of holomorphic functions / Studia Math 127(2):137~168
K. D. Bierstedt / 1993 / Biduals of weighted Banach spaces of analytic functions / J. Austral. Math. Soc. Ser. A 54(1):70~79
J. Bonet / 1998 / Composition operators between weighted Banach spaces of analytic functions / ustral. Math. Soc. Ser. A 64(1):101~118
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