Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Maximal operators and capacity


Author: David R. Adams
Journal: Proc. Amer. Math. Soc. 34 (1972), 152-156
MSC: Primary 42A92; Secondary 31B15
DOI: https://doi.org/10.1090/S0002-9939-1972-0350314-1
MathSciNet review: 0350314
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that many maximal functions defined on the $ {L_p}$ spaces are bounded operators on $ {L_p}$ if and only if they satisfy a capacitary weak type inequality.


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

  • [1] D. R. Adams and N. G. Meyers, Bessel potentials. Inclusion relations among classes of exceptional sets, Bull Amer. Math. Soc. 77 (1971), 968-970. MR 0284607 (44:1831)
  • [2] A.-P. Calderón, Lebesgue spaces of differentiate functions and distributions, Proc. Sympos. Pure Math., vol. 4, Amer. Math. Soc., Providence, R.I., 1961, pp. 33-49. MR 26 #603.
  • [3] L. Carleson, Maximal functions and capacities, Ann. Inst. Fourier (Grenoble) 15 (1965), fase. 1, 59-64. MR 32 #2602. MR 0185132 (32:2602)
  • [4] C. Fefferman, On the convergence of multiple Fourier series, Bull. Amer. Math. Soc. 77 (1971), 744-745. MR 0435724 (55:8682)
  • [5] B. Fuglede, Le théorème du minimax et la théorie fine du potentiel, Ann. Inst. Fourier (Grenoble) 15 (1965), fasc. 1, 65-88. MR 32 #7781. MR 0190368 (32:7781)
  • [6] R. A. Hunt, On the convergence of Fourier series, Proc. Conference Orthogonal Expansions and their Continuous Analogues (Edwardsville, Ill., 1967), Southern Illinois Univ. Press, Carbondale, Ill., 1968, pp. 235-255. MR 38 #6296. MR 0238019 (38:6296)
  • [7] N. G. Meyers, A theory of capacities for potentials of functions in Lebesgue classes, Math. Scand. 26 (1970), 255-292. MR 0277741 (43:3474)
  • [8] C. Preston, Some inequalities involving the Hardy-Littlewood maximal function in the theory of capacities, Proc. Sympos. Functional Analysis, Academic Press, New York, 1970. MR 0294675 (45:3743)
  • [9] P. Sjolin, Convergence almost everywhere of certain singular integrals and multiple Fourier series, Ark. Mat. 9 (1971), 65-90. MR 0336222 (49:998)
  • [10] A. Zygmund, Trigonometrical series. Vol. II, 2nd ed., Cambridge Univ. Press, New York, 1959. MR 21 #6498. MR 0076084 (17:844d)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42A92, 31B15

Retrieve articles in all journals with MSC: 42A92, 31B15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0350314-1
Keywords: Capacity, maximal functions, Fourier series, singular integrals, $ {L_p}$ spaces
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society