Weighted Bergman projections and tangential area integrals

Cohn, William

Cohn, William

Studia Mathematica, Tome 104 (1993), p. 59-76 / Harvested from The Polish Digital Mathematics Library

Résumé

Let Ω be a bounded strictly pseudoconvex domain in $ℂ^{n}$ . In this paper we find sufficient conditions on a function f defined on Ω in order that the weighted Bergman projection $P_{s} f$ belong to the Hardy-Sobolev space $H_{k}^{p} (\partial Ω)$ . The conditions on f we consider are formulated in terms of tent spaces and complex tangential vector fields. If f is holomorphic then these conditions are necessary and sufficient in order that f belong to the Hardy-Sobolev space $H_{k}^{p} (\partial Ω)$ .

Publié le : 1993-01-01

Zbl 0811.32001

EUDML-ID : urn:eudml:doc:216003

@article{bwmeta1.element.bwnjournal-article-smv106i1p59bwm,
     author = {William Cohn},
     title = {Weighted Bergman projections and tangential area integrals},
     journal = {Studia Mathematica},
     volume = {104},
     year = {1993},
     pages = {59-76},
     zbl = {0811.32001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv106i1p59bwm}
}

Cohn, William. Weighted Bergman projections and tangential area integrals. Studia Mathematica, Tome 104 (1993) pp. 59-76. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv106i1p59bwm/

Bibliographie

[00000] [AB] P. Ahern and J. Bruna, Maximal and area integral characterizations of Hardy-Sobolev spaces in the unit ball of $ℂ^{n}$ , Rev. Mat. Iberoamericana 4 (1988), 123-153. | Zbl 0685.42008

[00001] [AN] P. Ahern and A. Nagel, Strong $L^{p}$ estimates for maximal functions with respect to singular measures; with applications to exceptional sets, Duke Math. J. 53 (1986), 359-393. | Zbl 0601.32007

[00002] [AS1] P. Ahern and R. Schneider, Holomorphic Lipschitz functions in pseudoconvex domains, Amer. J. Math. 101 (1979), 543-565. | Zbl 0455.32008

[00003] [AS2] P. Ahern and R. Schneider, A smoothing property of the Henkin and Szegö projections, Duke Math. J. 47 (1980), 135-143. | Zbl 0453.32004

[00004] [B] F. Beatrous, Boundary estimates for derivatives of harmonic functions, Studia Math. 98 (1991), 55-71. | Zbl 0734.42011

[00005] [C] W. Cohn, Tangential characterizations of Hardy-Sobolev spaces, Indiana Univ. Math. J. 40 (1991), 1221-1249. | Zbl 0768.46017

[00006] [CMSt] R. Coifman, Y. Meyer and E. Stein, Some new function spaces and their applications to harmonic analysis, J. Funct. Anal. 62 (1985), 304-335. | Zbl 0569.42016

[00007] [GK] I. Gohberg and N. Krupnik, Einführung in die Theorie der eindimensionalen singulären Integraloperatoren, Birkhäuser, Basel 1979. | Zbl 0413.47040

[00008] [Gr] S. Grellier, Complex tangential characterizations of Hardy-Sobolev spaces of holomorphic functions, preprint. | Zbl 0779.32001

[00009] [KSt] N. Kerzman and E. M. Stein, The Szegö kernel in terms of Cauchy-Fantappiè kernels, Duke Math. J. 45 (1978), 197-223. | Zbl 0387.32009

[00010] [L] E. Ligocka, On the Forelli-Rudin construction and weighted Bergman projections, Studia Math. 94 (1989), 257-272. | Zbl 0688.32020

[00011] [Ra] M. Range, Holomorphic Functions and Integral Representations in Several Complex Variables, Springer, New York 1986. | Zbl 0591.32002

[00012] [Ru] W. Rudin, Function Theory in the Unit Ball of $ℂ^{n}$ , Springer, New York 1980.

[00013] [St1] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton 1970.

[00014] [St2] E. M. Stein, Some problems in harmonic analysis, in: Harmonic Analysis in Euclidean Spaces, Proc. Sympos. Pure Math. 35, Amer. Math. Soc., 1979, 3-19.

[00015] [St3] E. M. Stein, Boundary Behavior of Holomorphic Functions of Several Complex Variables, Math. Notes, Princeton Univ. Press, Princeton 1972.