Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the Littlewood-Paley $ g$-function and the Lusin $ s$-function


Author: George Gasper
Journal: Trans. Amer. Math. Soc. 134 (1968), 385-403
MSC: Primary 31.11
DOI: https://doi.org/10.1090/S0002-9947-1968-0235138-1
MathSciNet review: 0235138
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] N. Aronszajn and K. T. Smith, Functional spaces and functional completion, Ann. Inst. Fourier (Grenoble) 6 (1955), 125-185. MR 0080878 (18:319c)
  • [2] A. P. Calderón, On the behavior of harmonic functions at the boundary, Trans. Amer. Math. Soc. 68 (1950), 47-54.
  • [3] -, Commutators of singular integral operators, Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 1092-1099. MR 0177312 (31:1575)
  • [4] G. Gasper, Jr., On the Littlewood-Paley and Lusin functions in higher dimensions, Proc. Nat. Acad. Sci. U.S.A. 57 (1967), 25-28. MR 0206324 (34:6143)
  • [5] G. H. Hardy and J. E. Littlewood, A maximal theorem with function-theoretic applications, Acta Math. 54 (1930), 81-116. MR 1555303
  • [6] J. E. Littlewood and R. E. A. C. Paley, Theorems on Fourier series and power series, Part I, J. London Math. Soc. 6 (1931), 230-233; Part II, Proc. London Math. Soc. 42 (1937), 52-89; Part III, ibid. 43 (1937), 105-126.
  • [7] N. Lusin, Sur une propriété des fonctions à carré sommable, Bull. Calcutta Math. Soc. 20 (1930), 139-154.
  • [8] J. Marcinkiewicz and A. Zygmund, A theorem of Lusin, Duke Math. J. 4 (1938), 473-485. MR 1546069
  • [9] B. Muckenhoupt and E. M. Stein, Classical expansions and their relation to conjugate harmonic functions, Trans. Amer. Math. Soc. 118 (1965), 17-92. MR 0199636 (33:7779)
  • [10] I. Privaloff, Sur certaines classes de fonctions subharmoniques et leur représentation analytique, Dokl. Akad. Nauk. SSSR 2 (1938), 191-220.
  • [11] K. T. Smith, A generalization of an inequality of Hardy and Littlewood, Canad. J. Math. 8 (1956), 157-170. MR 0086889 (19:261e)
  • [12] E. M. Stein, On the functions of Littlewood-Paley, Lusin, and Marcinkiewicz, Trans. Amer. Math. Soc. 88 (1958), 430-466. MR 0112932 (22:3778)
  • [13] E. M. Stein and G. Weiss, On the theory of harmonic functions of several variables, I. Acta Math. 103 (1960), 25-62. MR 0121579 (22:12315)
  • [14] C. de la Vallée Poussin, Propriétés des fonctions harmoniques dans un domaine ouvert limité par des surfaces à courbure bornée, Ann. Scuola Norm. Sup. Pisa 2 (1933), 167-197.
  • [15] D. Waterman, On functions analytic in a half-plane, Trans. Amer. Math. Soc. 81 (1956), 167-194. MR 0076030 (17:834f)
  • [16] A. Zygmund, Proof of a theorem of Littlewood and Paley, Bull. Amer. Math. Soc. 51 (1945), 439-446. MR 0012306 (7:8b)
  • [17] -, Trigonometric series, Cambridge Univ. Press, New York, 1959.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 31.11

Retrieve articles in all journals with MSC: 31.11


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1968-0235138-1
Article copyright: © Copyright 1968 American Mathematical Society

American Mathematical Society