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Many scholars studied the boundedness of Ces\`{a}ro operators between $Q_K$ spaces and Bloch spaces of holomorphic functions in the unit disc in the complex plane, however, they did not describe the compactness. Let $0<\alpha<+\infty$, $K(r)$ be right continuous nondecreasing functions on $(0,+\infty)$ and satisfy $$\int_{0}^{1\over e}K(\log{1\over r})rdr<+\infty.$$Suppose $g$ is a holomorphic function in the unit disk. In this paper, some sufficient and necessary conditions for the extended Ces\`{a}ro operators $T_g$ between $\alpha$-Bloch spaces and $Q_K$ spaces in the unit disc to be bounded and compact are obtained.
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참고문헌 (22)
참고문헌 신청
C. C. Cowen / 1995 / Composition operators on spaces of analytic functions / CRC Press
M. Essen / 2002 / On analytic and meromorphic functions and spaces of QK-type / Illinois J. Math 46(4):1233~1258
M. Essen / 2006 / Seceral function-theoretic characterizations of M¨obius invariant QK spaces / J. Funct. Anal 230(1):78~115
Z. Fang / 2009 / Extended Ces´aro operators from generally weighted Bloch spaces to Zygmund spaces / J. Math. Anal. Appl 359(2):499~507
X. Guo / 2008 / Ces`aro operators on Hardy spaces in the unit ball / J. Math. Anal. Appl 339(1):1~9
M. Essen / 2002 / On analytic and meromorphic functions and spaces of QK-type / Illinois J. Math 46(4):1233~1258
M. Essen / 2006 / Seceral function-theoretic characterizations of M¨obius invariant QK spaces / J. Funct. Anal 230(1):78~115
Z. Fang / 2009 / Extended Ces´aro operators from generally weighted Bloch spaces to Zygmund spaces / J. Math. Anal. Appl 359(2):499~507
X. Guo / 2008 / Ces`aro operators on Hardy spaces in the unit ball / J. Math. Anal. Appl 339(1):1~9
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