×

On the distributions of bounded functions in the abstract Hardy space theory and some of their applications. (English) Zbl 0347.46055


MSC:

46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
30H05 Spaces of bounded analytic functions of one complex variable
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] B. DAVIS, On the distributions of conjugate functions of nonnegative measures, Duke Math. J., 40 (1973), 695-700. · Zbl 0271.60090 · doi:10.1215/S0012-7094-73-04062-3
[2] B. DAVIS, On the weak type (1, 1) inequality for conjugate functions, Proc. Amer. Math Soc., 44 (1974), 307-311. · Zbl 0259.42016 · doi:10.2307/2040426
[3] Y. KATZNELSON, An Introduction to Harmonic Analysis, Wiley, New York, 1968 · Zbl 0169.17902
[4] H. KONIG, Zur abstrakten Theorie der analytischen Funktionen, Math. Z., 88 (1965), 136-165. · Zbl 0132.09503 · doi:10.1007/BF01112096
[5] H. KONIG, Zur abstrakten Theorie der analytischen Funktionen II, Math. Ann., 16 (1966), 9-17. · Zbl 0135.35502 · doi:10.1007/BF02052482
[6] H. KONIG, Theory of abstract Hardy spaces, Lecture Notes, California Institute o Technology, Pasadena, 1967.
[7] H. KONIG, Generalized conjugate functions in abstract Hardy space theory.In: Journee de la Soc. Math. France, Algebres de fonctions, Grenoble, 11-16Septembre 1970, 36-44. · Zbl 0247.46063
[8] J. E. LITTLEWOOD, On functions subharmonic in a circle II, Proc. London Math. Soc., 28 (1928), 383-394. · JFM 54.0516.04
[9] S. K. PICHORIDES, On the conjugate of bounded functions, Bull. Amer. Math. Soc., 8 (1975), 143-144. · Zbl 0304.42013 · doi:10.1090/S0002-9904-1975-13675-5
[10] E. M. STEIN AND G. WEISS, An extension of a theorem of Marcinkiewicz and some o its applications, J. Math. Mech., 8 (1959), 263-284. · Zbl 0084.10801
[11] M. TSUJI, Potential Theory in Modern Function Theory, Maruzen, Tokyo, 1959 · Zbl 0087.28401
[12] K. YABUTA, Funktionen mit nichtnegativem Realteil in abstrakten Hardyalgebren, Arch Math. 24 (1973), 164-168. · Zbl 0262.30035 · doi:10.1007/BF01228194
[13] K. YABUTA, On the distribution of values of functions in some function classes in th abstract Hardy space theory, Thoku Math. J., 25 (1973), 89-102. · Zbl 0257.46076 · doi:10.2748/tmj/1178241417
[14] K. YABUTA, On bounded functions in the abstract Hardy space theory, Thoku Math J., 26 (1974), 77-84. · Zbl 0278.46044 · doi:10.2748/tmj/1178241236
[15] K. YABUTA, On bounded functions in the abstract Hardy space theory II, Thoku Math J., 26 (1974), 513-533. · Zbl 0299.46051 · doi:10.2748/tmj/1178241075
[16] K. YABUTA, On bounded functions in the abstract Hardy space theory III, Thok Math. J., 27 (1975), 111-128. · Zbl 0299.46052 · doi:10.2748/tmj/1178241041
[17] A, ZYGMUND, Trigonometric Series, 2nd ed. Cambridge Univ. Press, New York, 1968 Zentralblatt MATH: · Zbl 0628.42001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.