Geodesic
Integral Inequalities for Entire Functions of Exponential Type in Morrey Spaces
Informatics and Automation, Theory of Functions of Several Real Variables and Its Applications, Tome 323 (2023), pp. 87-106.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove analogs of Bernstein's inequalities and inequalities of different metrics and different dimensions for entire functions of exponential type. Such inequalities are well known for Lebesgue spaces. In this paper we prove them for Morrey spaces.
Keywords: entire functions of exponential type, integral inequalities, Morrey space. 
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V. I. Burenkov; D. J. Joseph. Integral Inequalities for Entire Functions of Exponential Type in Morrey Spaces. Informatics and Automation, Theory of Functions of Several Real Variables and Its Applications, Tome 323 (2023), pp. 87-106. http://geodesic.mathdoc.fr/item/TRSPY_2023_323_a4/

[1] O. V. Besov, V. P. Il'in, and S. M. Nikol'skii, Integral Representations of Functions and Imbedding Theorems, v. 1, 2, 1st ed., J. Wiley Sons, New York, 1978 | MR | MR | Zbl

[2] Burenkov V.I., Sobolev spaces on domains, Teubner-Texte Math., 137, B. G. Teubner, Stuttgart, 1997 | MR

[3] Burenkov V.I., “Recent progress in studying the boundedness of classical operators of real analysis in general Morrey-type spaces. I”, Eurasian Math. J., 3:3 (2012), 11–32 | MR | Zbl

[4] Burenkov V.I., “Recent progress in studying the boundedness of classical operators of real analysis in general Morrey-type spaces. II”, Eurasian Math. J., 4:1 (2013), 21–45 | MR | Zbl

[5] Burenkov V.I., Guliyev V.S., Tararykova T.V., “Comparison of Morrey spaces and Nikol'skii spaces”, Eurasian Math. J., 12:1 (2021), 9–20 | DOI | MR | Zbl

[6] Burenkov V.I., Joseph D.J., “Inequalities for entire functions of exponential type in Morrey spaces”, Eurasian Math. J., 13:3 (2022), 92–99 | DOI | MR | Zbl

[7] V. I. Burenkov and T. V. Tararykova, “An analog of Young's inequality for convolutions of functions for general Morrey-type spaces”, Proc. Steklov Inst. Math., 293 (2016), 107–126 | DOI | DOI | MR | Zbl

[8] M. L. Gol'dman, “The description of traces for certain function spaces”, Proc. Steklov Inst. Math., 150 (1981), 105–133 | Zbl | Zbl

[9] Guliyev V.S., “Generalized weighted Morrey spaces and higher order commutators of sublinear operators”, Eurasian Math. J., 3:3 (2012), 33–61 | MR | Zbl

[10] Ibragimov I.I., “Ekstremalnye zadachi v klasse tselykh funktsii eksponentsialnogo tina”, UMN, 12:3 (1957), 323–328 | MR | Zbl

[11] I. I. Ibragimov, “Some inequalities for entire functions of exponential type”, Am. Math. Soc. Transl., Ser. 2,, 43 (1964), 155–167 | Zbl | Zbl

[12] Ibragimov I.I., Teoriya priblizheniya tselymi funktsiyami, Elm, Baku, 1979

[13] I. I. Ibragimov and A. S. Dzhafarov, “On some inequalities for an entire function of finite degree and its derivatives”, Sov. Math., Dokl., 2 (1961), 699–702 | MR | Zbl

[14] Lemarié-Rieusset P.-G., “The role of Morrey spaces in the study of Navier–Stokes and Euler equations”, Eurasian Math. J., 3:3 (2012), 62–93 | MR | Zbl

[15] Nikolskii S.M., “Nekotorye neravenstva dlya tselykh funktsii konechnoi stepeni mnogikh peremennykh i ikh primenenie”, DAN SSSR, 76:6 (1951), 785–788 | Zbl

[16] Nikolskii S.M., “Neravenstva dlya tselykh funktsii konechnoi stepeni i ikh primenenie v teorii differentsiruemykh funktsii mnogikh peremennykh”, Tr. MIAN, 38 (1951), 244–278 | Zbl

[17] S. M. Nikol'skii, Approximation of Functions of Several Variables and Imbedding Theorems, Grundl. Math. Wiss., 205, Springer, Berlin, 1975 | MR | Zbl

[18] Ragusa M.A., “Operators in Morrey type spaces and applications”, Eurasian Math. J., 3:3 (2012), 94–109 | MR | Zbl

[19] Sickel W., “Smoothness spaces related to Morrey spaces—a survey. I”, Eurasian Math. J., 3:3 (2012), 110–149 | MR | Zbl

[20] Sickel W., “Smoothness spaces related to Morrey spaces—a survey. II”, Eurasian Math. J., 4:1 (2013), 82–124 | MR | Zbl

[21] A. F. Timan, Theory of Approximation of Functions of a Real Variable, Pergamon Press, Oxford, 1963 | MR | Zbl

[22] V. S. Vladimirov, Equations of Mathematical Physics, URSS, Moscow, 1996 | MR | MR