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.
- 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 https://doi.org/10.1090/S0002-9904-1971-12821-5 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.
- 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 https://doi.org/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 https://doi.org/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 https://doi.org/10.1007/BF02383638
- Antoni Zygmund, Trigonometrical series, Chelsea Publishing Co., New York, 1952. 2nd ed. MR 0076084
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42A92, 31B15
Retrieve articles in all journals with MSC: 42A92, 31B15
Additional Information
Keywords:
Capacity,
maximal functions,
Fourier series,
singular integrals,
<IMG WIDTH="29" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${L_p}$"> spaces
Article copyright:
© Copyright 1972
American Mathematical Society