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Holomorphic Sobolev spaces on the ball

Seria
Rozprawy Matematyczne tom/nr w serii: 276 wydano: 1989
Zawartość
Warianty tytułu
Abstrakty
EN

CONTENTS
Introduction ..............................................................5
0. Preliminaries and notation....................................6
1. Hilbert spaces of holomorphic functions..............11
2. Some estimates ..................................................16
3. The space $L^p_q$............................................22
4. Norm estimates...................................................30
5. Sobolev norms....................................................35
6. Projections in Sobolev spaces............................47
References.............................................................56
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 276
Liczba stron
57
Liczba rozdzia³ów
Opis fizyczny
1989
Daty
wydano
1989
Twórcy
  • Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A
autor
  • Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A
Bibliografia
  • [1] R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975,
  • [2] N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1950), 337-404.
  • [3] F. Beatrous, Jr., and J. Burbea, Positive-definiteness and its applications to interpolation problems for holomorphic functions, Trans. Amer. Math. Soc. 284 (1984), 247-270.
  • [4] S. Bell, Biholomorphic mappings and the ∂̅-problem, Ann. Math. 114 (1981), 103-113.
  • [5] S. Bell and H. Boas, Regularity of the Bergman projection in weakly pseudoconvex domains, Math. Ann. 257 (181), 23-30.
  • [6] H. Boas, Holomorphic reproducing kernels in Reinhardt domains. Pacific J. Math. 112 (1984), 273-292.
  • [7] H. Boas, Sobolev space projections in strictly pseudoconvex domains, Trans. Amer. Math. Soc. 288 (1985), 227-240.
  • [8] J. Burbea and P. Masani, Banach and Hilbert Spaces of Vector-Valued Functions, Their General Theory and Applications to Holomorphy, Pitman Research Notes in Math., vol. 90, Pitman, London, 1984.
  • [9] R. R, Coifman and R. Rochberg, Representation theorems for holomorphic and harmonic functions in $L^p$, Asterisque 77 (1980), 11-66.
  • [10] R. R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. Math. 103 (1976), 611-635.
  • [11] P. L. Duren, Theory of $H^p$ Spaces, Academic Press, New York, 1970.
  • [12] T. M. Flett, On the rate of growth of mean values of holomorphic and harmonic functions, Proc. London Math. Soc. 20 (1970), 749-768.
  • [13] G. B. Folland and E. M. Stein, Estimates for the $∂̅_b$ complex and analysis on Heisenberg group, Comm. Pure Appl. Math. 27 (1974), 429-522.
  • [14] F. Forelli and W. Rudin, Projections on spaces of holomorphic functions in balls, Indiana Univ. Math. J. 24 (1974), 593-602.
  • [15] I. Graham, The radial derivative, fractional integrals, and the comparative growth of means of holomorphic functions on the unit ball in $C^n$, Recent Developments in Several Complex Variables, Annals, Math. Studies 100 (1981), 171-178.
  • [16] A, Korányi and S. Vági, Singular integrals in homogeneous spaces and some problems of classical analysis, Ann. Scuola Norm. Sup. Pisa 25 (1971), 575-648.
  • [17] S. G. Krantz, Analysis on the Heisenberg group and estimates for functions in Hardy classes of several complex variables. Math. Ann. 244 (1979), 243-262.
  • [18] J. E. Littlewood and R.E.A.C. Paley, Theorems on Fourier series and power series (ii), Proc. London Math. Soc. (2) 42 (1937), 52-89.
  • [19] W. Rudin, Function Theory in the Unit Ball of $C^n$, Springer-Verlag, New York, 1981.
  • [20] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, 1971.
  • [21] E. M. Stein, Boundary Behavior of Holomorphic Functions of Several Complex Variables, Princeton Univ. Press, Princeton, 1972
  • [22] F. G. Tricomi and A. Erdelyi, The asymptotic expansion of a ratio of gamma functions, Pacific J. Math. 1 (1951), 133-142.
Języki publikacji
EN
Uwagi
1980 Mathematics Subject Classification: Primary 32A35, 42B30, 32A10, 32H10, 46E35; Secondary 30D55, 26A16.
Identyfikator YADDA
bwmeta1.element.zamlynska-4fb0d52f-01ce-4230-ab22-edfdc9df9de4
Identyfikatory
ISBN
83-01-08873-7
ISSN
0012-3862
Kolekcja
DML-PL
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