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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  );
  • 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.


  • 주제어

    strongly pseudo convex domain .   integral means .   Levi polynomial.  

  • 참고문헌 (9)

    1. F. Beatrous, Estimates for Derivatives of Holomorphic Functions in Pseudoconvex Domains, Math. Z. 191 (1986), 91-116 
    2. 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 
    3. 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 
    4. H. R. Cho and E. G. Kwon, Growth rate of the functions in Bergman type spaces, J. Math. Anal. Appl. 285 (2003), 275-281 
    5. P. L. Duren, Theory of $H^p$ spaces, Academic Press, New York, 1970 
    6. M. M. Peloso, Hankel operators on weighted Bergman spaces on strongly domains, Illinois J. Math. 38 (1994), no. 2, 223-249 
    7. R. M. Range, Holomorphic functions and integral representations in several complex variables, Springer-Verlag, Berlin, 1986 
    8. 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 
    9. F. Beatrous, $L^p$ estimates for extensions of holomorphic functions, Michigan Math. J. 32 (1985), 361-380 

 저자의 다른 논문

  • Cho, Hong-Rae (19)

    1. 1990 "COMPLEX HOLOMORPHIC LINE BUNDLES AND PSEUDOCONVEXITY" The Pusan Kyongnam mathematical journal 6 (2): 155~158    
    2. 1990 "PROPERTIES OF A FAMILY OF WEAKLY PSEUDOCONVEX MANIFOLDS" The Pusan Kyongnam mathematical journal 6 (1): 101~110    
    3. 1993 "VANISHING THEOREM FOR COHOMOLOGY GROUPS AND STEIN-NESS PROBLEM" Communications of the Korean Mathematical Society = 대한수학회논문집 8 (4): 679~687    
    4. 1994 "STEIN-NESS OF OPEN SUBSETS IN COMPLEX SPACES OF FINITE DIMENSION" Journal of the Korean Mathematical Society = 대한수학회지 31 (1): 131~138    
    5. 1995 "GLOBAL REGULARITY OF THE $\={\partial}$-NEUMANN PROBLEM ON PSEUDOCONVEX COMPLEX MANIFOLDS" The Pusan Kyongnam mathematical journal 11 (2): 125~131    
    6. 1995 "APPROXIMATION BY HOLOMORPHIC FUNCTIONS ON PSEUDOCONVEX COMPLEX MANIFOLDS" Bulletin of the Korean Mathematical Society = 대한수학회보 32 (2): 259~263    
    7. 1995 "STABILITY OF THE BERGMAN KERNEL FUNCTION ON PSEUDOCONVEX DOMAINS IN $C^n$" Communications of the Korean Mathematical Society = 대한수학회논문집 10 (2): 349~355    
    8. 2003 "EMBEDDING OF WEIGHTED $L^p$ SPACES AND THE $\bar{\partial}$-PROBLEM" East Asian mathematical journal 19 (1): 73~80    
    9. 2003 "SOBOLEV-TYPE EMBEDDING THEOREMS FOR HARMONIC AND HOLOMORPHIC SOBOLEV SPACES" Journal of the Korean Mathematical Society = 대한수학회지 40 (3): 435~445    
    10. 2006 "A BMO TYPE CHARACTERIZATION OF WEIGHTED LIPSCHITZ FUNCTIONS IN TERMS OF THE BEREZIN TRANSFORM" Communications of the Korean Mathematical Society = 대한수학회논문집 21 (3): 419~428    

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