Hardy-Sobolev spaces and maximal functions

Akihiko MIYACHI

doi:10.2969/jmsj/04210073

Akihiko MIYACHI

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JOURNAL FREE ACCESS

1990 Volume 42 Issue 1 Pages 73-90

DOI https://doi.org/10.2969/jmsj/04210073

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Published: 1990 Received: October 21, 1988 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor Hiroshi Fujita on the occasion of his sixtieth birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) A. P. Calderón, Estimates for singular integral operators in terms of maximal functions, Studia Math., 44 (1972), 563-582.
2) A. P. Calderón and R. Scott, Sobolev type inequalities for p>0, Studia Math., 62 (1978), 75-92.
3) R. A. DeVore and R. C. Sharpley, Maximal functions measuring smoothness, Mem. Amer. Math. Soc., 293, Amer. Math. Soc., Providence, 1984.
4) D. Goldberg, A local version of real Hardy spaces, Duke Math. J., 46 (1979), 27-42.
5) V. G. Krotov, On differentiability of functions in L^p, 0<p<1, (Russian), Mat. Sb., 117 (159) (1982), 95-113, (English Transl., Math. USSR-Sb., 45 (1983), 101-119).
6) H. Kumano-go, Pseudo-Differential Operators, MIT Press, Cambridge-Massachusetts-London, 1981.
7) K. Masuda, Nonlinear Elliptic Equations, (Japanese), Iwanami Kôza Kiso Sûgaku, Iwanami Shoten, Tokyo, 1977.
8) A. Miyachi, Maximal functions for distributions on open sets, Hitotsubashi J. Arts Sci., 28 (1987), 45-58.
9) A. Miyachi, H^p spaces over open subsets of Rⁿ, to appear in Studia Math.
10) J. Peetre, Classes de Hardy sur les variétés, C. R. Acad. Sci. Paris, 280 (1975), A439-A441.
11) E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, 1970.
12) E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, 1971.

Right : [1] A. P. Calderón, Estimates for singular integral operators in terms of maximal functions, Studia Math., 44 (1972), 563-582.
[2] A. P. Calderón and R. Scott, Sobolev type inequalities for p>0, Studia Math., 62 (1978), 75-92.
[3] R. A. DeVore and R. C. Sharpley, Maximal functions measuring smoothness, Mem. Amer. Math. Soc., 293, Amer. Math. Soc., Providence, 1984.
[4] D. Goldberg, A local version of real Hardy spaces, Duke Math. J., 46 (1979), 27-42.
[5] V. G. Krotov, On differentiability of functions in L^p, 0<p<1, (Russian), Mat. Sb., 117 (159) (1982), 95-113, (English Transl., Math. USSR-Sb., 45 (1983), 101-119).
[6] H. Kumano-go, Pseudo-Differential Operators, MIT Press, Cambridge-Massachusetts-London, 1981.
[7] K. Masuda, Nonlinear Elliptic Equations, (Japanese), Iwanami Kôza Kiso Sûgaku, Iwanami Shoten, Tokyo, 1977.
[8] A. Miyachi, Maximal functions for distributions on open sets, Hitotsubashi J. Arts Sci., 28 (1987), 45-58.
[9] A. Miyachi, H^p spaces over open subsets of Rⁿ, to appear in Studia Math.
[10] J. Peetre, Classes de Hardy sur les variétés, C. R. Acad. Sci. Paris, 280 (1975), A439-A441.
[11] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, 1970.
[12] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, 1971.

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