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)

 
 

 

On hypersingular integrals and certain spaces of locally differentiable functions


Author: Richard L. Wheeden
Journal: Trans. Amer. Math. Soc. 146 (1969), 211-230
MSC: Primary 47.70; Secondary 46.00
DOI: https://doi.org/10.1090/S0002-9947-1969-0253098-5
MathSciNet review: 0253098
Full-text PDF

References | Similar Articles | Additional Information

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

  • [1] A. P. Calderón, On the behavior of harmonic functions at the boundary, Trans. Amer. Math. Soc. 68 (1950), 47-54.
  • [2] -, ``Lebesgue spaces of functions and distributions'' in Partial differential equations, Proc. Sympos. Pure Math., Vol. 4, Amer. Math. Soc., Providence, R. I., 1961, pp. 33-49.
  • [3] A. P. Calderón and A. Zygmund, Singular integral operators and differential equations, Amer. J. Math. 79 (1957), 901-921. MR 0100768 (20:7196)
  • [4] -, Local properties of solutions of elliptic partial differential equations, Studia Math. 20 (1961), 171-225. MR 0136849 (25:310)
  • [5] -, Unpublished lecture notes.
  • [6] A. Erdelyi et al., Higher transcendental functions, Vol. 2, (Bateman manuscript project), McGraw-Hill, New York, 1953.
  • [7] Y. Sagher, On hypersingular integrals with complex homogeneity, Thesis, Univ. of Chicago, Chicago, Ill., 1967.
  • [8] E. M. Stein, The characterization of functions arising as potentials, Bull. Amer. Math. Soc. 67 (1961), 102-104. MR 0123729 (23:A1051)
  • [9] -, On the theory of harmonic functions of several variables. II. Behavior near the boundary, Acta Math. 106 (1961), 137-174. MR 0173019 (30:3234)
  • [10] -, Singular integrals, harmonic functions, and differentiability properties of functions of several variables, Proc. Sympos. Pure Math., Vol. 10, Amer. Math. Soc., Providence, R. I., 1968.
  • [11] E. M. Stein and A. Zygmund, On the fractional derivatives of functions, Proc. London Math. Soc. 14A (1965), 249-264. MR 0177076 (31:1340)
  • [12] M. Weiss, On symmetric derivatives in $ {L^p}$, Studia Math. 24 (1964), 89-100. MR 0162094 (28:5295)
  • [13] M. Weiss and A. Zygmund, On the existence of conjugate functions of higher order, Fund. Math. 48 (1960), 175-187. MR 0113093 (22:3934)
  • [14] 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)
  • [15] -, On hypersingular integrals and Lebesgue spaces of differentiable functions. II, Trans. Amer. Math. Soc. 139 (1969), 37-53. MR 0240682 (39:2028)
  • [16] A. Zygmund, Trigonometric series, 2nd ed., Vol. 2, Cambridge Univ. Press, Cambridge, 1959. MR 0107776 (21:6498)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 47.70, 46.00

Retrieve articles in all journals with MSC: 47.70, 46.00


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1969-0253098-5
Article copyright: © Copyright 1969 American Mathematical Society

American Mathematical Society