PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1991 | 54 | 3 | 271-297
Tytuł artykułu

Norm and Taylor coefficients estimates of holomorphic functions in balls

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A classical result of Hardy and Littlewood states that if $f(z) = ∑_{m=0}^{∞} a_m z^m$ is in $H^p$, 0 < p ≤ 2, of the unit disk of ℂ, then $∑_{m=0}^{∞} (m+1)^{p-2}|a_m|^p ≤ c_p ∥f∥_p^p$ where $c_p$ is a positive constant depending only on p. In this paper, we provide an extension of this result to Hardy and weighted Bergman spaces in the unit ball of $ℂ^n$, and use this extension to study some related multiplier problems in $ℂ^n$.
Słowa kluczowe
Twórcy
  • Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
  • Korea Institute of Technology, 400 Gusong-Dong, Chung-Ku, Taejon, Korea 300-31, U.S.A.
Bibliografia
  • [1] F. Beatrous and J. Burbea, Holomorphic Sobolev spaces on the ball, Dissertationes Math. 276 (1989).
  • [2] R. R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. of Math. 103 (1976), 611-635.
  • [3] P. L. Duren, Theory of $H^p$ Spaces, Academic Press, New York 1970.
  • [4] P. L. Duren and A. L. Shields, Properties of $H^p$ (0 < p < 1) and its containing Banach space, Trans. Amer. Math. Soc. 141 (1969), 255.
  • [5] P. L. Duren and A. L. Shields,Coefficient multipliers of $H^p$ and $B^p$ spaces, Pacific J. Math. 32 (1970), 69-78.
  • [6] T. M. Flett, On the rate of growth of mean values of holomorphic and harmonic functions, Proc. London Math. Soc. 20 (1970), 749.
  • [7] F. Forelli and W. Rudin, Projections on the spaces of holomorphic functions in balls, Indiana Univ. Math. J. 24 (1974), 593-602.
  • [8] G. H. Hardy and J. E. Littlewood, Theorems concerning mean values of analytic or harmonic functions, Quart. J. Math. Oxford Ser. 12 (1942), 221-256.
  • [9] A. Korányi and S. Vagi, Singular integrals in homogeneous spaces and some problems of classical analysis, Ann. Scuola Norm. Sup. Pisa 25 (1971), 575-648.
  • [10] E. M. Stein and G. Weiss, On the interpolation of analytic families of operators acting on $H^p$ spaces, Tôhoku Math. J. (2) 9 (1957), 318-339.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv54z3p271bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.