Hiroshima Mathematical Journal

Bernstein's theorem and translation invariant operators

Bui Huy Qui

Full-text: Open access

Article information

Source
Hiroshima Math. J., Volume 11, Number 1 (1981), 81-96.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206134219

Digital Object Identifier
doi:10.32917/hmj/1206134219

Mathematical Reviews number (MathSciNet)
MR606835

Zentralblatt MATH identifier
0473.46020

Subjects
Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems
Secondary: 42B15: Multipliers

Citation

Qui, Bui Huy. Bernstein's theorem and translation invariant operators. Hiroshima Math. J. 11 (1981), no. 1, 81--96. doi:10.32917/hmj/1206134219. https://projecteuclid.org/euclid.hmj/1206134219


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References

  • [1] J. Bergh and J. Lofstrom, Interpolation spaces, Springer-Verlag, Berlin-Heidelberg- New York, 1976.
  • [2] A. Beurling, Construction and analysis of some convolution algebras, Ann. Inst. Fourier 14 (1964), fasc. 2, 1-32.
  • [3] Bui Huy Qui, Some aspects of weighted and non-weighted Hardy spaces, Kkyroku Res. Inst. Math. Sci. Kyoto Univ. 383 (1980), 38-56.
  • [4] T. M. Flett, Temperatures, Bessel potentials and Lipschitz spaces, Proc. London Math. Soc. 22(1971), 385-451.
  • [5] T. M. Flett, Temperatures, Some elementary inequalities for integrals with applications to Fourier transforms, ibid. 29 (1974), 538-556.
  • [6] J. E. Gilbert, Interpolationbetween weighted L*>-spaces, Ark. Mat. 10 (1972), 235-249.
  • [7] D. Goldberg, A local version of real Hardy spaces, Duke Math. J. 46 (1979), 27-42.
  • [8] C. S. Herz, Lipschitz spaces and Bernstein's theorem on absolutely convergent Fourier transforms, J. Math. Mech. 18 (1968), 283-324.
  • [9] R. Johnson, Temperatures, Riesz potentials, and the Lipschitz spaces of Herz, Proc. London Math. Soc. 27 (1973), 209-316.
  • [10] R. Johnson, Temperatures, Lipschitz spaces, Littlewood-Paley spaces, and convoluteurs, ibid. 29 (1974), 127-141.
  • [11] R. Johnson, Temperatures, Multipliers of HP spaces, Ark. Mat. 16 (1978), 235-249.
  • [12] T. Mizuhara, Fourier transforms on Lipschitz spaces and Littlewood-Paley spaces, J. London Math. Soc. 17 (1978), 87-101.
  • [13] J. Peetre, Hp spaces, Lectures notes, Lund, 1974 (corrected ed., 1975).
  • [14] E. M. Stein and A. Zygmund, Boundedness of translation invariant operators on Holder spaces and Z^-spaces, Ann. of Math. 85 (1967), 337-349.
  • [15] M. H. Taibleson, On the theory of Lipschitz spaces of distributions on Euclidean «-space. I. Principal properties; II. Translation invariant operators, duality, and interpolation; III. Smoothness and integrabilityof Fourier transforms, smoothness of convolution kernels, J. Math. Mech. 13 (1964), 407-479; 14 (1965), 821-839; 15 (1966), 973-981.
  • [16] H. Triebel, Spaces of Besov-Hardy-Sobolev type, Teubner-Texte Math., Teubner, Leipzig, 1978.
  • [17] H. Triebel, On Besov-Hardy-Sobolev spaces in domains and regular ellipticboundary value problems. The case 0</?<oo, Comm. Partial Differential Equations 3 (1978), 1083-1164.
  • [18] T. Mizuhara, Inhomogeneous Littlewood-Paley spaces K(a p, q preprint.