The Lp-boundedness of pseudodifferential operators with estimates of parabolic type and product type

Masao YAMAZAKI

doi:10.2969/jmsj/03820199

The L^p-boundedness of pseudodifferential operators with estimates of parabolic type and product type

Masao YAMAZAKI

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JOURNAL FREE ACCESS

1986 Volume 38 Issue 2 Pages 199-225

DOI https://doi.org/10.2969/jmsj/03820199

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Published: 1986 Received: May 18, 1984 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: CITATION Details: Wrong : 1) J. Bergh and J. Löfström, Interpolation spaces, Springer-Verlag, Berlin-Heidelberg -New York, 1976.
2) G. Bourdaud, L^p-estimates for certain non-regular pseudo-differential operators, Comm. Partial Differential Equations, 7 (1982), 1023-1033.
3) A. P. Calderón and A. Torchinsky, Parabolic maximal functions associated with a distribution, I, Adv. in Math., 16(1975), 1-64; II, Adv. in Math., 24 (1977), 101-171.
4) R. R. Coifman et Y. Meyer, Au-délà des opérateurs pseudo-différentiels, Astèrisque, 57, Soc. Math. France, Paris, 1978.
5) E. B. Fabes and N. M. Rivière, Singular integrals with mixed homogeneity, Studia Math., 27 (1966), 19-38.
6) R. Fefferman, Singular integrals on product domains, Bull. Amer. Math. Soc. (New Series), 4 (1981), 195-201.
7) R. Fefferman and E. M. Stein, Singular integrals on product spaces, Adv. in Math., 45 (1982), 117-143.
8) S. Mossaheb et M. Okada, Une classe d'opérateurs pseudo-différentiels bornés sur L^r(Rⁿ), 1<r<∞, C. R. Acad. Sci. Paris, 285 (1977), 613-616.
9) T. Muramatu and M. Nagase, On sufficient conditions for the boundedness of pseudo-differential operators, Proc. Japan Acad. Ser. A, 55 (1979), 293-296.
10) M. Nagase, The L^p-boundedness of pseudo-differential operators with non-regular symbols, Comm. Partial Differential Equations, 2 (1977), 1045-1061.
11) E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, New Jersey, 1970.
12) H. Triebel, Interpolation theory, function spaces, differential operators, North-Holland, Amsterdam-New York-Oxford, 1978.
13) M. Yamazaki, Continuité des opérateurs pseudo-différentiels et para-différentiels dans les espaces de Besov et les espaces de Triebel-Lizorkin non-isotropes, C. R. Acad. Sci. Paris Sér. I, 296 (1983), 533-536.
14) M. Yamazaki, A quasi-homogeneous version of paradifferential operators, I, II, to appear in J. Fac. Sci. Univ. Tokyo.
15) M. Yamazaki, The L^p-boundedness of pseudo-differential operators satisfying estimates of parabolic type and product type, Proc. Japan Acad. Ser. A, 60 (1984), 279-282.

Right : [1] J. Bergh and J. Löfström, Interpolation spaces, Springer-Verlag, Berlin-Heidelberg -New York, 1976.
[2] G. Bourdaud, L^p-estimates for certain non-regular pseudo-differential operators, Comm. Partial Differential Equations, 7 (1982), 1023-1033.
[3] A. P. Calderón and A. Torchinsky, Parabolic maximal functions associated with a distribution, I, Adv. in Math., 16 (1975), 1-64; II, Adv. in Math., 24 (1977), 101-171.
[4] R. R. Coifman et Y. Meyer, Au-délà des opérateurs pseudo-différentiels, Astèrisque, 57, Soc. Math. France, Paris, 1978.
[5] E. B. Fabes and N. M. Rivière, Singular integrals with mixed homogeneity, Studia Math., 27 (1966), 19-38.
[6] R. Fefferman, Singular integrals on product domains, Bull. Amer. Math. Soc. (New Series), 4 (1981), 195-201.
[7] R. Fefferman and E. M. Stein, Singular integrals on product spaces, Adv. in Math., 45 (1982), 117-143.
[8] S. Mossaheb et M. Okada, Une classe d'opérateurs pseudo-différentiels bornés sur L^r(Rⁿ), 1<r<∞, C. R. Acad. Sci. Paris, 285 (1977), 613-616.
[9] T. Muramatu and M. Nagase, On sufficient conditions for the boundedness of pseudo-differential operators, Proc. Japan Acad. Ser. A, 55 (1979), 293-296.
[10] M. Nagase, The L^p-boundedness of pseudo-differential operators with non-regular symbols, Comm. Partial Differential Equations, 2 (1977), 1045-1061.
[11] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, New Jersey, 1970.
[12] H. Triebel, Interpolation theory, function spaces, differential operators, North-Holland, Amsterdam-New York-Oxford, 1978.
[13] M. Yamazaki, Continuité des opérateurs pseudo-différentiels et para-différentiels dans les espaces de Besov et les espaces de Triebel-Lizorkin non-isotropes, C. R. Acad. Sci. Paris Sér. I, 296 (1983), 533-536.
[14] M. Yamazaki, A quasi-homogeneous version of paradifferential operators, I, II, to appear in J. Fac. Sci. Univ. Tokyo.
[15] M. Yamazaki, The L^p-boundedness of pseudo-differential operators satisfying estimates of parabolic type and product type, Proc. Japan Acad. Ser. A, 60 (1984), 279-282.

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