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)

 
 

 

An interpolation theorem and a sharp form of a multilinear fractional integration theorem


Author: Jong-Guk Bak
Journal: Proc. Amer. Math. Soc. 120 (1994), 435-441
MSC: Primary 46E30; Secondary 26A33, 42A38, 46M35
DOI: https://doi.org/10.1090/S0002-9939-1994-1182696-X
MathSciNet review: 1182696
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove a sharp interpolation theorem for Orlicz spaces with the Luxemburg norm. As a corollary we obtain a sharp form of an exponential integrability theorem, due to Grafakos, for the multilinear fractional integration operator. This generalizes a theorem of Adams.


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

  • [A] D. Adams, A sharp inequality of J. Moser for higher order derivatives, Ann. of Math. (2) 128 (1988), 385-398. MR 960950 (89i:46034)
  • [G] L. Grafakos, On multilinear fractional integrals, Studia Math. (to appear). MR 1164632 (93d:42021)
  • [KR] M. A. Krasnosel'skii and Ya. B. Rutickii, Convex functions and Orlicz spaces, Groningen, 1961.
  • [M] J. Musielak, Orlicz spaces and modular spaces, Springer-Verlag, New York, 1983. MR 724434 (85m:46028)
  • [R] M. M. Rao, Interpolation, ergodicity, and martingales, J. Math. Mech. 16 (1966), 543-567. MR 0207960 (34:7773)
  • [S] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, NJ, 1970. MR 0290095 (44:7280)
  • [SW] E. M. Stein and G. Weiss, An introduction to Fourier analysis on Euclidean spaces, Princeton Univ. Press, Princeton, NJ, 1971. MR 0304972 (46:4102)
  • [Y] K. Yosida, Functional analysis, 6th ed., Springer-Verlag, New York, 1980. MR 617913 (82i:46002)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46E30, 26A33, 42A38, 46M35

Retrieve articles in all journals with MSC: 46E30, 26A33, 42A38, 46M35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1182696-X
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society