Interpolation in the Nevanlinna and Smirnov classes and harmonic majorants

Andreas Hartmann; Xavier Massaneda; Artur Nicolau; Pascal Thomas

doi:10.1016/j.jfa.2004.02.015

Interpolation in the Nevanlinna and Smirnov classes and harmonic majorants

Journal of Functional Analysis ◽

10.1016/j.jfa.2004.02.015 ◽

2004 ◽

Vol 217 (1) ◽

pp. 1-37 ◽

Cited By ~ 7

Author(s):

Andreas Hartmann ◽

Xavier Massaneda ◽

Artur Nicolau ◽

Pascal Thomas

Keyword(s):

Smirnov Classes ◽

Harmonic Majorants

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A note on n-harmonic majorants

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700010340 ◽

1986 ◽

Vol 34 (3) ◽

pp. 461-472

Author(s):

Hong Oh Kim ◽

Chang Ock Lee

Keyword(s):

Harmonic Function ◽

Complex Plane ◽

Unit Disc ◽

Dirichlet Integral ◽

Harmonic Majorant ◽

Harmonic Majorants

Suppose D (υ) is the Dirichlet integral of a function υ defined on the unit disc U in the complex plane. It is well known that if υ is a harmonic function in U with D (υ) < ∞, then for each p, 0 < p < ∞, |υ|p has a harmonic majorant in U.We define the “iterated” Dirichlet integral Dn (υ) for a function υ on the polydisc Un of Cn and prove the polydisc version of the well known fact above:If υ is an n-harmonic function in Un with Dn (υ) < ∞, then for each p, 0 < p < ∞, |υ|p has an n-harmonic majorant in Un.

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Part I. Harmonic Majorants Part II. Nevanlinna and Hardy-Orlicz Classes

Topics in Hardy Classes and Univalent Functions ◽

10.1007/978-3-0348-8520-1_3 ◽

1994 ◽

pp. 35-53

Author(s):

Marvin Rosenblum ◽

James Rovnyak

Keyword(s):

Harmonic Majorants

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A problem of Burkholder and the existence of harmonic majorants of |x|^p in certain domains in R^d

Annales Academiae Scientiarum Fennicae Series A I Mathematica ◽

10.5186/aasfm.1984.0906 ◽

1984 ◽

Vol 9 ◽

pp. 107-116 ◽

Cited By ~ 6

Author(s):

Matts Essén ◽

Kersti Haliste

Keyword(s):

Harmonic Majorants

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Faber-Laurent Series in Variable Smirnov Classes

TURKISH JOURNAL OF MATHEMATICS ◽

10.3906/mat-1911-87 ◽

2020 ◽

Keyword(s):

Laurent Series ◽

Smirnov Classes

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The Fréchet envelopes of vector-valued Smirnov classes

Studia Mathematica ◽

10.4064/sm-94-2-163-177 ◽

1989 ◽

Vol 94 (2) ◽

pp. 163-177 ◽

Cited By ~ 3

Author(s):

M. Nawrocki

Keyword(s):

Smirnov Classes ◽

Vector Valued

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Holomorphic Spaces in the Unit Ball of

Journal of Function Spaces and Applications ◽

10.1155/2013/725705 ◽

2013 ◽

Vol 2013 ◽

pp. 1-14 ◽

Cited By ~ 2

Author(s):

Augusto Guadalupe Miss Paredes ◽

Lino Feliciano Reséndis Ocampo ◽

Luis Manuel Tovar Sánchez

Keyword(s):

Unit Ball ◽

Holomorphic Functions ◽

Vector Spaces ◽

Spaces Of Holomorphic Functions ◽

Harmonic Majorants

We introduce the and vector spaces of holomorphic functions defined in the unit ball of , generalizing previous work like Ouyang et al. (1998), Stroethoff (1989), and Choa et al. (1992). Likewise, we characterize those spaces in terms of harmonic majorants as a generalization of Arellano et al. (2000).

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