zbMATH — the first resource for mathematics

Weighted distribution spaces and pseudodifferential operators. (English) Zbl 0474.35089

35S05 Pseudodifferential operators as generalizations of partial differential operators
65H10 Numerical computation of solutions to systems of equations
46E15 Banach spaces of continuous, differentiable or analytic functions
46E20 Hilbert spaces of continuous, differentiable or analytic functions
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46F05 Topological linear spaces of test functions, distributions and ultradistributions
Full Text: DOI
[1] R. Beals,Spatially inhomogeneous pseudodifferential operators, II, Comm. Pure Appl. Math.27 (1974), 161–205. · Zbl 0283.35071 · doi:10.1002/cpa.3160270204
[2] R. Beals,A general calculus of pseudodifferential operators, Duke Math. J.42 (1975), 1–42. · Zbl 0343.35078 · doi:10.1215/S0012-7094-75-04201-5
[3] R. Beals,Characterization of pseudodifferential operators and applications, Duke Math. J.44 (1977), 45–57;correction, Duke Math. J.46 (1979), 215. · Zbl 0353.35088 · doi:10.1215/S0012-7094-77-04402-7
[4] R. Beals,L p and Hölder estimates for pseudodifferential operators: necessary conditions, Proc. Symp. Pure Math., Vol. 35, part 2, Amer. Math. Soc., Providence, R.I., 1979, pp. 153–157. · Zbl 0418.35085
[5] R. Beals,L p and Hölder estimates for pseudodifferential operators: sufficient conditions, Ann. Inst. Fourier29 (1979), 239–260. · Zbl 0387.35065
[6] R. Beals and C. Fefferman,Spatially inhomogeneous pseudodifferential operators, Comm. Pure Appl. Math.27 (1974), 1–24. · Zbl 0279.35071 · doi:10.1002/cpa.3160270102
[7] A. P. Calderón,Intermediate spaces and interpolation, the complex method, Studia Math.24 (1964), 113–190. · Zbl 0204.13703
[8] R. Coifman and G. Weiss,Analyse Harmonique Non-Commutative sur certains Espaces Homogènes, Lecture Notes in Math., No. 242, Springer-Verlag, Berlin, 1971. · Zbl 0224.43006
[9] R. Coifman and G. Weiss,Extensions of Hardy spaces and their uses in analysis, Bull. Amer. Math. Soc.83 (1977), 569–645. · Zbl 0358.30023 · doi:10.1090/S0002-9904-1977-14325-5
[10] C. Folland,Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Mat.13 (1975), 161–207. · Zbl 0312.35026 · doi:10.1007/BF02386204
[11] G. Folland and E. M. Stein, Estimates for the \(\bar \partial _b \) complex and analysis on the Heisenberg group, Comm. Pure Appl. Math.27 (1974), 429–522. · Zbl 0293.35012 · doi:10.1002/cpa.3160270403
[12] L. Hörmander,Pseudo-differential operators and hypoelliptic equations, Proc. Symp. Pure Math., Vol. 10, Amer. Math. Soc., Providence, R.I., 1967, pp. 138–183.
[13] L. Hörmander,The Weyl calculus of pseudodifferential operators, Com. Pure Appl. Math.32 (1979), 359–443. · Zbl 0396.47029 · doi:10.1002/cpa.3160320304
[14] N. Lerner,Sur les espaces de Sobolev généraux associés aux classes récentes d’opérateurs pseudo-différentiels, C. R. Acad. Sci. Paris, Sér. A,289 (1979), 663–666.
[15] A. Nagel and E. M. Stein,A new class of pseudodifferential operators, Proc. Nat. Acad. Sci. U.S.A.75 (1978), 582–585. · Zbl 0376.35053 · doi:10.1073/pnas.75.2.582
[16] L. Rothschild and E. M. Stein,Hypoelliptic differential operators and nilpotent groups, Acta Math.137 (1976), 247–320. · Zbl 0346.35030 · doi:10.1007/BF02392419
[17] R. Seeley,Complex powers of an elliptic operator, Proc. Symp. Pure Math., Vol. 10, Amer. Math. Soc., Providence, R. I., 1967, pp. 288–307. · Zbl 0159.15504
[18] V. A. Solonnikov,A priori estimates for solutions of second-order equations of parabolic type, Trudy Mat. Inst. Steklov70 (1964), 133–212. · Zbl 0168.08202
[19] A. Unterberger,Symboles associés aux champs de repères de la forme symplectique, C. R. Acad. Sci. Paris, Sér. A,245 (1977), 1005–1008. · Zbl 0381.47025
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.