On the $L^{2}$-boundedness of pseudo-differential operators
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- by A. G. Childs PDF
- Proc. Amer. Math. Soc. 61 (1976), 252-254 Request permission
Abstract:
A. P. Calderón and R. Vaillancourt have established ${L^2}$-boundedness in case the symbol has bounded partial derivatives to order $3$ in any variable. H. O. Cordes has proved ${L^2}$-boundedness if this order is $1$. It is shown here that it suffices for the symbol to satisfy a uniform Hölder continuity condition of order $\tfrac {1} {2} + \delta ,\;\delta > 0$.References
- Alberto-P. Calderón and Rémi Vaillancourt, On the boundedness of pseudo-differential operators, J. Math. Soc. Japan 23 (1971), 374–378. MR 284872, DOI 10.2969/jmsj/02320374
- H. O. Cordes, On compactness of commutators of multiplications and convolutions, and boundedness of pseudodifferential operators, J. Functional Analysis 18 (1975), 115–131. MR 377599, DOI 10.1016/0022-1236(75)90020-8
- A. G. Childs, On the $L^{2}$-boundedness of pseudo-differential operators, Proc. Amer. Math. Soc. 61 (1976), no. 2, 252–254 (1977). MR 442755, DOI 10.1090/S0002-9939-1976-0442755-2
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 61 (1976), 252-254
- MSC: Primary 47G05; Secondary 35S05
- DOI: https://doi.org/10.1090/S0002-9939-1976-0442755-2
- MathSciNet review: 0442755