Lp-boundedness of pseudo-differential operators satisfying Besov estimates I

Mitsuru SUGIMOTO

doi:10.2969/jmsj/04010105

L^p-boundedness of pseudo-differential operators satisfying Besov estimates I

Mitsuru SUGIMOTO

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ジャーナルフリー

1988 年 40 巻 1 号 p. 105-122

DOI https://doi.org/10.2969/jmsj/04010105

詳細

Published: 1988 Received: 1986/03/14 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) J. Bergh and J. Löfström, Interpolation Spaces, Grundlehren der math. Wiss., 223, Springer, 1976.
2) A. P. Calderón and R. Vaillancourt, On the boundedness of pseudo-differential operators, J. Math. Soc. Japan, 23 (1971), 374-378.
3) A. G. Childs, On the L²-boundedness of pseudo-differential operators, Proc. Amer. Math. Soc., 61 (1976), 252-254.
4) R. R. Coifman and Y. Meyer, Au-delà des opérateurs pseudo-différentiels, Astérisque57, Société math. France, 1978.
5) H. O. Cordes, On compactness of commutators of multiplications and convolutions, and boundedness of pseudodifferential operators, J. Funct. Anal., 18 (1975), 115-131.
6) L. Hörmander, Pseudo-differential operators and hypoelliptic equations, Proc. Symp. on Singular Integrals, Amer. Math. Soc., 10 (1967), 138-183.
7) T. Kato, Boundedness of some pseudo-differential operators, Osaka J. Math., 13 (1976), 1-9.
8) H. Kumano-go, Pseudo-differential Operators, MIT Press, Cambridge, 1982.
9) J. Löfström, Interpolation of weighted spaces of differentiable functions on R^d, Ann. Mat. Pura Appl., 132 (1982), 189-214.
10) A. Miyachi, Estimates for pseudo-differential operators of class S_0,0, to appear in Math. Nachr.
11) T. Muramatu, Estimates for the norm of pseudo-differential operators by means of Besov spaces, Lecture Notes in Math., 1256 (1987), 330-349.
12) J. Peetre, New Thoughts on Besov Spaces, Duke Univ. Math. Ser. 1, Math. Dept. Duke Univ., Durham, 1976.
13) M. Sugimoto, L^p-boundedness of pseudo-differential operators satisfying Besov estimates II, to appear in J. Fac. Sci. Univ. Tokyo
14) H. Triebel, Theory of Function Spaces, Monogr. in Math., 78, Birkhäuser Verlag, Basel-Boston-Stuttgart, 1983.

Right : [1] J. Bergh and J. Löfström, Interpolation Spaces, Grundlehren der math. Wiss., 223, Springer, 1976.
[2] A. P. Calderón and R. Vaillancourt, On the boundedness of pseudo-differential operators, J. Math. Soc. Japan, 23 (1971), 374-378.
[3] A. G. Childs, On the L²-boundedness of pseudo-differential operators, Proc. Amer. Math. Soc., 61 (1976), 252-254.
[4] R. R. Coifman and Y. Meyer, Au-delà des opérateurs pseudo-différentiels, Astérisque 57, Société math. France, 1978.
[5] H. O. Cordes, On compactness of commutators of multiplications and convolutions, and boundedness of pseudodifferential operators, J. Funct. Anal., 18 (1975), 115-131.
[6] L. Hörmander, Pseudo-differential operators and hypoelliptic equations, Proc. Symp. on Singular Integrals, Amer. Math. Soc., 10 (1967), 138-183.
[7] T. Kato, Boundedness of some pseudo-differential operators, Osaka J. Math., 13 (1976), 1-9.
[8] H. Kumano-go, Pseudo-differential Operators, MIT Press, Cambridge, 1982.
[9] J. Löfström, Interpolation of weighted spaces of differentiable functions on R^d, Ann. Mat. Pura Appl., 132 (1982), 189-214.
[10] A. Miyachi, Estimates for pseudo-differential operators of class S_0,0, to appear in Math. Nachr.
[11] T. Muramatu, Estimates for the norm of pseudo-differential operators by means of Besov spaces, Lecture Notes in Math., 1256 (1987), 330-349.
[12] J. Peetre, New Thoughts on Besov Spaces, Duke Univ. Math. Ser. 1, Math. Dept. Duke Univ., Durham, 1976.
[13] M. Sugimoto, L^p-boundedness of pseudo-differential operators satisfying Besov estimates II, to appear in J. Fac. Sci. Univ. Tokyo
[14] H. Triebel, Theory of Function Spaces, Monogr. in Math., 78, Birkhäuser Verlag, Basel-Boston-Stuttgart, 1983.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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