p -spaces of harmonic functions
Annales de l'Institut Fourier, Volume 17 (1967) no. 2, pp. 425-469.

Sous les hypothèses standard de l’axiomatique Brelot, étude de classes de fonctions harmoniques complexes définies comme les classes de Hardy classiques. Caractérisation comme solutions de problèmes de Dirichlet avec la frontière minimale, les filtres fins, et données-frontière dans L p , pour 1<p+, comme intégrales de mesures complexes finies sur la frontière minimale, pour p=1. Existence presque-partout à la frontière minimale d’une limite fine finie L p . Application à deux théorèmes du type F. et M. Riesz et Phragmen-Lindelöf pour fonctions positives “fortement sous harmoniques”, et à la classification des espaces harmoniques.

@article{AIF_1967__17_2_425_0,
     author = {Lumer-Na{\"\i}m, Linda},
     title = {${\mathcal {H}}^p$-spaces of harmonic functions},
     journal = {Annales de l'Institut Fourier},
     pages = {425--469},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {17},
     number = {2},
     year = {1967},
     doi = {10.5802/aif.276},
     mrnumber = {37 #1642},
     zbl = {0153.43102},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.276/}
}
TY  - JOUR
AU  - Lumer-Naïm, Linda
TI  - ${\mathcal {H}}^p$-spaces of harmonic functions
JO  - Annales de l'Institut Fourier
PY  - 1967
SP  - 425
EP  - 469
VL  - 17
IS  - 2
PB  - Institut Fourier
PP  - Grenoble
UR  - http://archive.numdam.org/articles/10.5802/aif.276/
DO  - 10.5802/aif.276
LA  - en
ID  - AIF_1967__17_2_425_0
ER  - 
%0 Journal Article
%A Lumer-Naïm, Linda
%T ${\mathcal {H}}^p$-spaces of harmonic functions
%J Annales de l'Institut Fourier
%D 1967
%P 425-469
%V 17
%N 2
%I Institut Fourier
%C Grenoble
%U http://archive.numdam.org/articles/10.5802/aif.276/
%R 10.5802/aif.276
%G en
%F AIF_1967__17_2_425_0
Lumer-Naïm, Linda. ${\mathcal {H}}^p$-spaces of harmonic functions. Annales de l'Institut Fourier, Volume 17 (1967) no. 2, pp. 425-469. doi : 10.5802/aif.276. http://archive.numdam.org/articles/10.5802/aif.276/

[1] H. Bauer, Axiomatische Behandlung des Dirichletschen Problems fur elliptische und parabolische Differential gleichungen, Math. Ann., 146 (1962), 1-59. | EuDML | MR | Zbl

[2] M. Brelot, Lectures on potential theory, Tata Institute of Fundamental Research, 19 (1960). | MR | Zbl

[3] M. Brelot, Intégrabilité uniforme. Quelques applications à la théorie du potentiel, Séminaire théorie du Potentiel, Paris, 6 (1961-1962). | EuDML | Numdam | Zbl

[4] M. Brelot, Axiomatique des fonctions harmoniques, Séminaire Mathématiques Supérieures, Université de Montréal, Eté 1965. | Zbl

[5] J. L. Doob, Probability methods applied to the first boundary value problem, Third Berkeley Symp. on Math. Statistics and Probability, 2 (1954-1955), 49-80. | MR | Zbl

[6] J. L. Doob, Conditional Brownian motion and the boundary limits of harmonic functions, Bull. Soc. Math. de France, 85 (1957), 431-458. | EuDML | Numdam | MR | Zbl

[7] J. L. Doob, A non probabilistic proof of the relative Fatou theorem, Ann. Inst. Fourier, 9 (1959), 295-299. | EuDML | Numdam | MR | Zbl

[8] J. L. Doob, Boundary properties of functions with finite Dirichlet integral, Ann. Inst. Fourier, 12 (1962), 573-621. | EuDML | Numdam | MR | Zbl

[9] J. L. Doob , Some classical function theory theorems and their modern versions, Colloque de Potentiel, Paris-Orsay, 1964, and Ann. Inst. Fourier, 15. 1 (1965), 113-136. | EuDML | Numdam | MR | Zbl

[10] L. Garding and L. Hormander, Strongly subharmonic functions, Math. scand., 15 (1964), 93-96. | Zbl

[11] K. Gowrisankaran, Extreme harmonic functions and boundary value problems, Ann. Inst. Fourier, 13, 2 (1963), 307-356. | Numdam | MR | Zbl

[12] K. Gowrisankaran, Fatou-Naim-Doob limit theorems in the axiomatic system of Brelot, Ann. Inst. Fourier, 16, 2 (1967). | Numdam | MR | Zbl

[13] R. M. Hervé, Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel, Ann. Inst. Fourier, 12 (1962), 415-571. | Numdam | MR | Zbl

[14] K. Hofmann, Banach spaces of analytic functions, Prentice-Hall (1962). | Zbl

[15] P. A. Lœb, An axiomatic treatment of pairs of elliptic differential equations, Ann. Inst. Fourier, 16, 2 (1967). | Numdam | Zbl

[16] P. A. Lœb and B. Walsh, The equivalence of Harnack's principle and Harnack's inequality in the axiomatic system of Brelot, Ann. Inst. Fourier, 15, 2 (1965), 597-600. | Numdam | MR | Zbl

[17] P. A. Lœb and B. Walsh, Decomposition of functions and the classification of spaces in axiomatic potential theory, Notices AMS, January 1966, 146.

[18] L. Lumer-Naim, Harmonic product and harmonic boundary for bounded complex-valued harmonic functions, Notices AMS, april 1965, 355.

[19] L. Lumer-Naim, Hp spaces of harmonic functions, Notices AMS, June 1966, 481.

[20] W. A. Luxemburg, Banach function spaces, Thesis, Van Gorcum, Assen, Netherlands. | Zbl

[21] R. S. Martin, Minimal positive harmonic functions, Trans. Amer. Math. Soc., 49 (1941), 137-172. | JFM | MR | Zbl

[22] M. Parreau, Sur les moyennes des fonctions harmoniques et analytiques et la classification des surfaces de Riemann, Ann. Inst. Fourier, 3 (1951), 103-197. | Numdam | MR | Zbl

[23] E. M. Stein and G. Weiss, On the theory of harmonic functions of several variables, I, Acta Math., 103 (1960), 25-62. | MR | Zbl

Cited by Sources: