대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제20권2호
  • /
  • Pages.339-350
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  • 2005
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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INEQUALITIES FOR THE INTEGRAL MEANS OF HOLOMORPHIC FUNCTIONS IN THE STRONGLY PSEUDOCONVEX DOMAIN

  • CHO, HONG-RAE (Department of Mathematics Pusan National University) ;
  • LEE, JIN-KEE (Department of Mathematics Education Andong National University)
  • 발행 : 2005.04.01
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초록

We obtain the following two inequalities on a strongly pseudoconvex domain $\Omega\;in\;\mathbb{C}^n\;:\;for\;f\;{\in}\;O(\Omega)$ $$\int_{0}^{{\delta}0}t^{a{\mid}a{\mid}+b}M_p^a(t, D^{a}f)dt\lesssim\int_{0}^{{\delta}0}t^{b}M_p^a(t,\;f)dt\;\int_{O}^{{\delta}O}t_{b}M_p^a(t,\;f)dt\lesssim\sum_{j=0}^{m}\int_{O}^{{\delta}O}t^{am+b}M_{p}^{a}\(t,\;\aleph^{i}f\)dt$$. In [9], Shi proved these results for the unit ball in $\mathbb{C}^n$. These are generalizations of some classical results of Hardy and Littlewood.

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참고문헌

  1. F. Beatrous, $L^p$ estimates for extensions of holomorphic functions, Michigan Math. J. 32 (1985), 361-380 https://doi.org/10.1307/mmj/1029003244
  2. F. Beatrous, Estimates for Derivatives of Holomorphic Functions in Pseudoconvex Domains, Math. Z. 191 (1986), 91-116 https://doi.org/10.1007/BF01163612
  3. H. R. Cho, Estimates on the mean growth of Hp functions in convex domains of finite type, Proc. Amer. Math. Soc. 131 (2003), no. 8, 2393-2398
  4. H. R. Cho and E. G. Kwon, Sobolev-type embedding theorems for harmonic and holomorphic Sobolev spaces, J. Korean Math. Soc. 40 (2003), no. 3, 435-445 https://doi.org/10.4134/JKMS.2003.40.3.435
  5. H. R. Cho and E. G. Kwon, Growth rate of the functions in Bergman type spaces, J. Math. Anal. Appl. 285 (2003), 275-281 https://doi.org/10.1016/S0022-247X(03)00416-5
  6. P. L. Duren, Theory of $H^p$ spaces, Academic Press, New York, 1970
  7. M. M. Peloso, Hankel operators on weighted Bergman spaces on strongly domains, Illinois J. Math. 38 (1994), no. 2, 223-249
  8. R. M. Range, Holomorphic functions and integral representations in several complex variables, Springer-Verlag, Berlin, 1986
  9. J. H. Shi, Inequalities for the integral means of holomorphic functions and their derivatives in the unit ball of Cn, Trans. Amer. Math. Soc. 328 (1991), no. 2, 619-637 https://doi.org/10.2307/2001797

피인용 문헌

  1. On Traces in Some Analytic Spaces in Bounded Strictly Pseudoconvex Domains vol.2015, 2015, https://doi.org/10.1155/2015/265245