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Table of contents for this issue | Previous article | Next article André Unterberger; Julianne UnterbergerHölder estimates and hypoellipticityAnnales de l'institut Fourier, 26 no. 2 ( 1976), p. 35-54, doi: 10.5802/aif.613
Article PDF | Reviews MR 54 #5611 | Zbl 0318.35018 | 1 citation in Cedram
The aim of this paper is to show how, in order to prove regularity theorems, Hölder estimates, i.e. estimates involving products of powers of different semi-norms, can be used as well as standard estimates, and may in some instances be casier to prove.
[1] R. BEALS and C. FEFFERMAN, Spatially inhomogeneous pseudo-differential operators I, Comm. Pure Appl. Math., 27 (1974), 1-24. MR 50 #5234 | Zbl 0279.35071[2] K. O. FRIEDRICHS, with the assistance of R. Vaillancourt, Pseudo-differential operators, Lecture Notes, N. Y. Univ., 1968. [3] L. HÖRMANDER, Linear partial differential operators, Springer Verlag, 1963. Zbl 0108.09301[4] L. HÖRMANDER, On the singularities of solutions of partial differential equations with constant coefficients, Symp. on linear partial differential operators, Jerusalem, June 1972. [5] L. HÖRMANDER, On the existence and regularity of solutions of linear pseudo-differential equations, L'Enseignement Mathématique, 17 (2) (1971), 99-163. MR 48 #9458 | Zbl 0224.35084[6] L. HÖRMANDER, Hypoelliptic second-order differential equations, Acta Math., 119 (1967), 147-171. MR 36 #5526 | Zbl 0156.10701[7] F. JOHN, Continuous dependance on data for solutions of partial differential equations with a prescribed bound, Comm. Pure Appl. Math., 13 (1960), 551-585. MR 24 #A317 | Zbl 0097.08101[8] J. KOHN, Pseudo-differential operators and hypoellipticity, Proc. Symp. Pure Math., 23 (1973), 61-69. MR 49 #3356 | Zbl 0262.35007[9] H. KUMANO-GO, Algebras of pseudo-differential operators, J. Fac. Sci. Univ. Tokyo, 17 (1970), 31-50. MR 45 #984 | Zbl 0206.10501[10] A. UNTERBERGER, Résolution d'équations aux dérivées partielles dans des espaces de distributions d'ordre de régularité variable, Ann. Inst. Fourier, 21 (1971), 85-128. Cedram | MR 58 #29043 | Zbl 0205.43104[11] A. UNTERBERGER, Ouverts stablement convexes par rapport à un opérateur différentiel, Ann. Inst. Fourier, 22 (1972), 269-290. Cedram | MR 49 #11022 | Zbl 0228.35014[12] K. WATANABE, On the boundedness of pseudo-differential operators of type ρ, δ with 0 ≤ ρ ˭ δ ˂ 1, Tôhoku Math. J., 25 (1973), 339-345. Article | MR 49 #5948 | Zbl 0284.35068
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