## Proceedings of the Japan Academy

### Estimates from $W_{p,\alpha }$ to $W_{q,\beta }$ for the solution of the Petrovskii Well posed Cauchy problems

Hitoshi Ishii

#### Article information

Source
Proc. Japan Acad., Volume 49, Number 9 (1973), 705-710.

Dates
First available in Project Euclid: 20 November 2007

https://projecteuclid.org/euclid.pja/1195519183

Digital Object Identifier
doi:10.3792/pja/1195519183

Mathematical Reviews number (MathSciNet)
MR0336457

Zentralblatt MATH identifier
0285.35012

Subjects
Primary: 47G05
Secondary: 35S10: Initial value problems for pseudodifferential operators

#### Citation

Ishii, Hitoshi. Estimates from $W_{p,\alpha }$ to $W_{q,\beta }$ for the solution of the Petrovskii Well posed Cauchy problems. Proc. Japan Acad. 49 (1973), no. 9, 705--710. doi:10.3792/pja/1195519183. https://projecteuclid.org/euclid.pja/1195519183

#### References

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• [2] P. Brenner: The Cauchy problem for systems in Lp and LPta. Ark. Mat., 2(1), 75-101 (1973).
• [3] I. M. Gelfand and G. E. Shilov: Generalized Functions, Vol. III. Academic Press, New York (1967).
• [4] L. Hormander: Estimates for translation invariant operators in L? spaces* Acta Math., 104, 93-139 (1960).
• [5] L. Hormander: Pseudo-differential operators and hypoelliptic equations. Amer. Math. Soc. Proc. Symp. Pure Math., 10, 138-183 (1967).
• [6] L. Hormander: On the existence and the regularity of solutions of linear pseudo-differential equations. Enseignement Math., 17, 99-163 (1971).
• [7] H. Ishii; On some Fourier multipliers and partial differential equations (to appear).
• [8] S. Sjostrand: On the Riesz means of the solution of the Schrodinger equation. Ann. Scuola Norm. Sup. Pisa, 24, 331-348 (1970).
• [9] E. M. Stein: Singular Integrals and Differentiability Properties of Functions. Princeton University Press, New Jersey (1970).
• [10] S. Wainger: Special trigonometric series in ^-dimensions. Mem. Amer. Math. Soc, no. 59 (1965).