A Dirichlet norm inequality and some inequalities for reproducing kernel spaces

Author:
Jacob Burbea

Journal:
Proc. Amer. Math. Soc. **83** (1981), 279-285

MSC:
Primary 30C40; Secondary 30H05, 46E20

MathSciNet review:
624914

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be analytic and of finite Dirichlet norm in the unit disk with . Then, for any ,

**[1]**N. Aronszajn,*Theory of reproducing kernels*, Trans. Amer. Math. Soc.**68**(1950), 337–404. MR**0051437**, 10.1090/S0002-9947-1950-0051437-7**[2]**Jacob Burbea,*On the Bergman metrics and their indicatrixes*, Duke Math. J.**39**(1972), 9–18. MR**0294684****[3]**Jacob Burbea,*Total positivity of certain reproducing kernels*, Pacific J. Math.**67**(1976), no. 1, 101–130. MR**0442662****[4]**Jacob Burbea,*The curvatures of the analytic capacity*, J. Math. Soc. Japan**29**(1977), no. 4, 755–761. MR**0460624****[5]**Saburou Saitoh,*Some inequalities for analytic functions with a finite Dirichlet integral on the unit disc*, Math. Ann.**246**(1979/80), no. 1, 69–77. MR**554132**, 10.1007/BF01352026

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1981-0624914-0

Keywords:
Dirichlet norm,
reproducing kernel spaces

Article copyright:
© Copyright 1981
American Mathematical Society