Summary
In this paper, we give necessary and sufficient conditions for a Carleman class in metricL p to be included in another or to be differentiable.
Similar content being viewed by others
References
Agmon, S.,Sur l'équivalence des classes de fonctions indéfiniment dérivables sur un demi-axe. C.R. Acad. Sci. Paris230 (1950), 350.
Bruna, J.,On inverse-closed algebras of infinitely differentiable functions. Studia Math.69 (1980), 61–67.
Carleman, T.,Les fonctions quasianlytiques. Gauthier-Villars, Paris, 1926.
Cartan, H. andMandelbrojt, S.,Solution du problème d'équivalence des classes de fonctions indéfiniment dérivables. Acta Math72 (1940), 31–39.
Chernoff, P. R.,Optimal Landau — Kolmogorov inequalities for dissipative operators in Hilbert and Banach spaces. Adv. in Math.34 (1979), 137–144.
Certain, M. W. andKurtz, T. G.,Landau — Kolomogorov inequalities for semi-groups. Proc. Amer. Math. Soc.63 (1977), 226–230.
Ditzian, Z.,Some remarks on inequalities of Landau and Kolmogorov. Aequationes Math.12 (1975), 213–238.
Gabushin, V. N.,Inequalities for norms of a function and its derivatives in the L p -metrics. (Russian). Mat. Zametki1 (1967), 291–298; English translation: Math. Notes1 (1967), 194–198.
Gorny, A.,Contribution à l'étude des fonctions dérivables d'une variable réelle. Acta Math.71 (1939), 317–358.
Hörmander, L.,The analysis of linear partial differential operators I. Springer-Verlag, Berlin—Heidelberg—New York, 1983.
Komatsu, H.,Ultradistributions. I. Structure theorems and a characterization. J. Fac. Sci. Univ. Tokyo Sect. IA Math.20 (1973), 25–105.
Kuptsov, N. P.,Exact constants in inequalities between norms of functions and their derivatives. Mat. Zametki41 (1987), 313–319; English translation: Math. Notes41 (1987), 178–182.
Lions, J. L. andMagenes, E.,Non-homogeneous boundary value problems and applications I, II, III. Springer-Verlag, Berlin—Heidelberg—New York, 1972–1973.
Manderlbrojt, S.,Séries adhérentes, régularisations des suites, applications. Gauthier-Villars, Paris, 1952.
Siddiqi, J. A.,On the equivalence of classes of infinitely differentiable functions. Izv. Akad. Nauk Armyan. SSR Ser. Mat.19 (1983), 19–30, 333, English translation: Soviet J. Contemporary Math. Anal.19 (1984), 18–29, 69.
Siddiqi, J. A. andElkoutri, A.,Norm inequalities for generators of analytic semigroups and cosine operator functions. Canad. Math. Bull.32 (1989), 47–53.
Stechkin, S. B.,Inequalities between the norms of derivatives of arbitrary function (Russian). Acta Sci. Math. (Szeged)26 (1965), 225–230.
Stein, E.,Functions of exponential type. Ann. of Math. (2)65 (1957), 585–595.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Siddiqi, J.A. Inclusion and differentiability criteria forL p-classes of infinitely differentiable functions. Aeq. Math. 40, 235–247 (1990). https://doi.org/10.1007/BF02112297
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02112297