Holomorphic Sobolev spaces on the ball

Beatrous, Frank; Burbea, Jacob

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Tytuł książki

Holomorphic Sobolev spaces on the ball

Autorzy

Frank Beatrous Jacob Burbea

Seria

Rozprawy Matematyczne tom/nr w serii: 276 wydano: 1989

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Abstrakty

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

Słowa kluczowe

Hardy spaces weighted Bergman spaces Sobolev spaces Bergman kernel Szegö kernel Poisson-Szegö kernel reproducing kernel Hardy-Littlewood type estimates BMO estimates

Tematy

Kategoryzacja MSC:

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Seria

Rozprawy Matematyczne tom/nr w serii: 276

Liczba stron

Liczba rozdzia³ów

Opis fizyczny

1989

Daty

wydano

1989

Twórcy

autor

Frank Beatrous

Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A

autor

Jacob Burbea

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

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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