Products of composition and differentiation between Hardy spaces

By Shuichi Ohno. 2006

101 citations recorded by the source corpus.

CvDf(z) = (Cf'Kz) = f(<p(z)) and DCvf(z) = (Cvf)'(z) = f{v{z))<p\z) for z e U and analytic function / on U. On a general space of analytic functions, D is typically unbounded. On the other hand, it has been showed that C9 is bounded on various spaces of analytic functions on Received 19th October, 2005 The author is partially supported by Grant-in-Aid for Scientific Research (No.17540169), Japan Society for the Promotion of Science. The author would like to thank the referee for the suggestions for improving the paper more explicitly. Copyright Clearance Centre, Inc. Serial-fee code: 0004-9727/06 SA2.00+0.00.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f70ba4873324d45475d4f737a113a68437424b34

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In Applied Mathematics

1. S. Stević
2. Xiangling Zhu
3. Yutian Wu
4. Hasi Wulan
5. Songxiao Li
6. Weifeng Yang
7. Steven G. Krantz
8. Lothar Berg

In Mathematical Physics

1. S. Stević
2. Xiangling Zhu
3. Yutian Wu
4. Hasi Wulan

Citations in the corpus

• Products of composition and differentiation operators on the weighted Bergman space (2009, background): “Products of integral, differentiation and composition operators on spaces of analytic functions are studied in [4, 5, 11, 12, 13, 14, 16, 19, 29, 31, 34, 35].”
• Generalized Weighted Composition Operators on Weighted Bergman Spaces (2009, background): “When n = 1 and u(z) = 1, then Dn ,u = C D which was studied in [5, 10].”
• Products of differentiation and composition operators on the Bloch space (2012, background): “The boundedness and compactness of the operators DCφ and Cφ D on Hardy and Bergman spaces were investigated in [2] and [7].”