Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Hypersingular integrals and parabolic potentials


Author: Sagun Chanillo
Journal: Trans. Amer. Math. Soc. 267 (1981), 531-547
MSC: Primary 46E35; Secondary 42B20
DOI: https://doi.org/10.1090/S0002-9947-1981-0626488-1
MathSciNet review: 626488
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we characterize the potential spaces associated with the heat equation in terms of singular integrals of mixed homogeneity.


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

  • [1] R. J. Bagby, Lebesgue spaces of parabolic potential, Illinois J. Math. 15 (1971), 610-634. MR 0291792 (45:883)
  • [2] E. B. Fabes and N. M. Riviere, Singular integrals with mixed homogeneity, Studia Math. 27 (1966), 19-38. MR 0209787 (35:683)
  • [3] B. F. Jones, Jr., Lipschitz spaces and the heat equation, J. Math. Mech. 18 (1968), 379-410. MR 0511929 (58:23543)
  • [4] C. H. Sampson, A characterization of parabolic Lebesgue spaces, Dissertation, Rice Univ., Houston, Tx.
  • [5] E. M. Stein, The characterization of functions arising as potentials. I, Bull. Amer. Math. Soc. 67 (1961), 102-104. MR 0123729 (23:A1051)
  • [6] -, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, N. J., 1970. MR 0290095 (44:7280)
  • [7] R. S. Strichartz, Multipliers on fractional Sobolev spaces, J. Math. Mech. 16 (1967), 1031-1060. MR 0215084 (35:5927)
  • [8] R. L. Wheeden, On hypersingular integrals and Lebesgue spaces of differentiable functions. I, Trans. Amer. Math. Soc. 134 (1968), 421-436. MR 0232249 (38:575)
  • [9] -, On hypersingular integrals and Lebesgue spaces of differentiable functions. II, Trans. Amer. Math. Soc. 139 (1969), 37-53. MR 0240682 (39:2028)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46E35, 42B20

Retrieve articles in all journals with MSC: 46E35, 42B20


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1981-0626488-1
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society