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)

 
 

 

On certain convolution inequalities


Author: Lars Inge Hedberg
Journal: Proc. Amer. Math. Soc. 36 (1972), 505-510
MSC: Primary 46E30; Secondary 46E35
DOI: https://doi.org/10.1090/S0002-9939-1972-0312232-4
MathSciNet review: 0312232
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is proved that certain convolution inequalities are easy consequences of the Hardy-Littlewood-Wiener maximal theorem. These inequalities include the Hardy-Littlewood-Sobolev inequality for fractional integrals, its extension by Trudinger, and an interpolation inequality by Adams and Meyers. We also improve a recent extension of Trudinger's inequality due to Strichartz.


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)
  • [1a] -, Bessel potentials. Inclusion relations among classes of exceptional sets (to appear).
  • [2] E. Gagliardo, Ulteriori proprietà di alcune classi di funzioni in più variabili, Ricerche Mat. 8 (1959), 24-51. MR 22 #181. MR 0109295 (22:181)
  • [3] G. H. Hardy and J. E. Littlewood, Some properties of fractional integrals. I, Math. Z. 27 (1928), 565-606. MR 1544927
  • [4] J. A. Hempel, G. R. Morris and N. S. Trudinger, On the sharpness of a limiting case of the Sobolev imbedding theorem, Bull. Austral. Math. Soc. 3 (1970), 369-373. MR 0280998 (43:6717)
  • [5] I. I. Hirschman, Jr., A convexity theorem for certain groups of transformations, J. Analyse Math. 2 (1953), 209-218. MR 15, 295; 1139. MR 0057936 (15:295b)
  • [6] J. Moser, A sharp form of an inequality by N. Trudinger, Indiana Univ. Math. J. 20 (1971), 1077-1092. MR 0301504 (46:662)
  • [7] L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa (3) 13 (1959), 115-162. MR 22 #823. MR 0109940 (22:823)
  • [8] S. L. Sobolev, On a theorem of functional analysis, Mat. Sb. 4 (46) (1938), 471-497; English transl., Amer. Math. Soc. Transl. (2) 34 (1963), 39-68.
  • [9] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton, Univ. Press, Princeton, N.J., 1970. MR 0290095 (44:7280)
  • [10] R. S. Strichartz, A note on Trudinger's extension of Sobolev's inequalities, Indiana Univ. Math. J. 21 (1972), 841-842. MR 0293389 (45:2466)
  • [11] N. S. Trudinger, On imbeddings into Orlicz spaces and some applications, J. Math. Mech. 17 (1967), 473-483. MR 35 #7121. MR 0216286 (35:7121)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46E30, 46E35

Retrieve articles in all journals with MSC: 46E30, 46E35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0312232-4
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society