Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the boundedness of pseudo differential operators in the class $ L\sp{m}\sb{\rho }{}\sb{,1}.$


Author: Luigi Rodino
Journal: Proc. Amer. Math. Soc. 58 (1976), 211-215
MSC: Primary 47G05; Secondary 35S05
DOI: https://doi.org/10.1090/S0002-9939-1976-0410480-X
MathSciNet review: 0410480
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that every pseudo differential operator in the class $ L_{\rho ,1}^m,0 \leq \rho \leq 1$, is bounded in $ {L^2}({{\mathbf{R}}^n})$ if and only if $ m < n(\rho - 1)/2$.


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

  • [1] A. P. Calderón and R. Vaillancourt, A class of bounded pseudo-differential operators, Proc. Nat. Acad. Sci. U.S.A. 69 (1972), 1185-1187. MR 45 #7532. MR 0298480 (45:7532)
  • [2] C. H. Ching, Pseudo-differential operators with nonregular symbols, J. Differential Equations 11 (1972), 436-447. MR 45 #5823. MR 0296764 (45:5823)
  • [3] L. Hörmander, Pseudo differential operators and hypoelliptic equations, Proc. Sympos. Pure Math., vol. 10, Amer. Math. Soc., Providence, R.I., 1967, pp. 138-183. MR 0383152 (52:4033)
  • [4] -, On the $ {L^2}$ continuity of pseudo-differential operators, Comm. Pure Appl. Math. 24 (1971), 529-535. MR 43 #6779. MR 0281060 (43:6779)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47G05, 35S05

Retrieve articles in all journals with MSC: 47G05, 35S05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0410480-X
Keywords: Pseudo differential operator, symbol of a pseudo differential operator, class $ S_{\rho ,\delta }^m$, class $ L_{\rho ,\delta }^m$
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society