Maximal operators and capacity

Adams, David R.

doi:10.1090/S0002-9939-1972-0350314-1

Maximal operators and capacity
HTML articles powered by AMS MathViewer

by David R. Adams

Proc. Amer. Math. Soc. 34 (1972), 152-156

DOI: https://doi.org/10.1090/S0002-9939-1972-0350314-1

PDF | Request permission

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

David R. Adams and Norman G. Meyers, Bessel potentials. Inclusion relations among classes of exceptional sets, Bull. Amer. Math. Soc. 77 (1971), 968–970. MR 284607, DOI 10.1090/S0002-9904-1971-12821-5

Lebesgue spaces of differentiate functions and distributions

26

Lennart Carleson, Maximal functions and capacities, Ann. Inst. Fourier (Grenoble) 15 (1965), no. fasc. 1, 59–64. MR 185132
Charles Fefferman, On the convergence of multiple Fourier series, Bull. Amer. Math. Soc. 77 (1971), 744–745. MR 435724, DOI 10.1090/S0002-9904-1971-12793-3
Bent Fuglede, Le théorème du minimax et la théorie fine du potentiel, Ann. Inst. Fourier (Grenoble) 15 (1965), no. fasc. 1, 65–88 (French). MR 190368
Richard A. Hunt, On the convergence of Fourier series, Orthogonal Expansions and their Continuous Analogues (Proc. Conf., Edwardsville, Ill., 1967) Southern Illinois Univ. Press, Carbondale, Ill., 1968, pp. 235–255. MR 0238019
Norman G. Meyers, A theory of capacities for potentials of functions in Lebesgue classes, Math. Scand. 26 (1970), 255–292 (1971). MR 277741, DOI 10.7146/math.scand.a-10981
C. Preston, Some inequalities involving the Hardy-Littlewood maximal function in a theory of capacities, Functional Analysis (Proc. Sympos., Monterey, Calif., 1969) Academic Press, New York, 1970, pp. 21–31. MR 0294675
Per Sjölin, Convergence almost everywhere of certain singular integrals and multiple Fourier series, Ark. Mat. 9 (1971), 65–90. MR 336222, DOI 10.1007/BF02383638
Antoni Zygmund, Trigonometrical series, Chelsea Publishing Co., New York, 1952. 2nd ed. MR 0076084