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The Bergman Metric and Related Bloch Spaces on the Exponentially Weighted Bergman Space
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We estimate the Bergman metric of the exponentially weighted Bergman spaceand prove many different geometric characterizations for related Bloch spaces. In particular, we prove that the Bergman metric of the exponentially weighted Bergman spaceis comparable to some Poincar'e type metric.
Abstract
We estimate the Bergman metric of the exponentially weighted Bergman spaceand prove many different geometric characterizations for related Bloch spaces. In particular, we prove that the Bergman metric of the exponentially weighted Bergman spaceis comparable to some Poincar'e type metric.
참고문헌 (9)
- Hicham Arroussi, "Reproducing Kernel Estimates, Bounded Projections and Duality on Large Weighted Bergman Spaces", The Journal of Geometric Analysis, 25(4), pp.2284~2312 (2015), Springer Science and Business Media LLC[DOI]
- A. Borichev, "Sampling and interpolation in large Bergman and Fock spaces", J. Funct. Aanl, 242, pp.563~606 (2007)
- M. Jarnicki, "Invariant distances and metrics in complex analysis, de Gruyter Expositions in Mathematics, 9" (1998), Walter de Gruyter & Co
- P. Lin, "Hankel operators on the weighted Bergman spaces with exponential type weights", Integr. Equ. Oper. Theory, 21, pp.460~483 (1995)
- N. Marco, "Intepolation and sampling sequence for entire functions", Geom. Funct. Anal, 13, pp.862~914 (2003)
- J. Pau, "Embedding theorems and integration operators on Bergman spaces with rapidly decreasing weights", J. Funct. Aanl, 259, pp.2727~2756 (2010)
- K. Zhu, "Bloch type spaces of analytic functions", Rocky Mountain J. Math, 23(3), pp.1143~1177 (1993)
- K. Zhu, "Distance and Banach space of holomorphic function on complex domains", J. London Math. Soc, 49, pp.163~182 (1994)
- K. Zhu, "Operator Theory in Function Spaces" (2007), American Mathematical Society
관련 논문AI추천
SOME NEW CHARACTERIZATIONS OF WEIGHTED BERGMAN SPACESSongxiao Li대한수학회 · 대한수학회보2010 · 제47권 제6호SOME REMARKS ON EXTREMAL PROBLEMS IN WEIGHTED BERGMAN SPACES OF ANALYTIC FUNCTIONS이현호, Milos Arsenovic, Romi F. Shamoyan대한수학회 · 대한수학회논문집2012 · 제27권 제4호Weighted Bloch spaces and some operators induced by radial derivatives강시호대한수학회 · 대한수학회보2004 · 제41권 제2호Norm of the composition operator from Bloch space to Bergman spaceKazuhiro Kasuga대한수학회 · 대한수학회논문집2014 · 제29권 제3호Some Toeplitz operators on weighted Bergman spaces강시호대한수학회 · 대한수학회보2011 · 제48권 제1호A characterization of weighted Bergman-Privalov spaces on the unit ball of $\mathbb{C}^n$Jun Miyazawa, Sei-ichiro Ueki, Yasuo Matsugu대한수학회 · 대한수학회지2002 · 제39권 제5호
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