Geodesic
Bernstein–Nikolskiĭ type inequality in Lorentz spaces and related topics
Vladikavkazskij matematičeskij žurnal, Tome 7 (2005) no. 2, pp. 90-100 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we study the Bernstein–Nikolskiĭ type inequality, the inverse Bernstein theorem and some properties of functions and their spectrum in Lorentz spaces $L^{p,q}(\mathbb{R}^n)$. 
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H. H. Bang; N. M. Cong. Bernstein–Nikolskiĭ type inequality in Lorentz spaces and related topics. Vladikavkazskij matematičeskij žurnal, Tome 7 (2005) no. 2, pp. 90-100. http://geodesic.mathdoc.fr/item/VMJ_2005_7_2_a9/

[1] Bang H. H., “A property of infinitely differentiable functions”, Proc. Amer. Math. Soc., 108 (1990), 71–78 | MR

[2] Bang H. H., “On the Bernstein–Nikolsky inequality, II”, Tokyo J. Math., 19 (1995), 123–151 | DOI | MR

[3] Bang H. H., “Functions with bounded spectrum”, Trans. Amer. Math. Soc., 347 (1995), 1067–1080 | DOI | MR | Zbl

[4] Bang H. H., “Spectrum of functions in Orlicz spaces”, J. Math. Sci. Univ. Tokyo, 4 (1997), 341–349 | MR | Zbl

[5] Izv. Math., 61, 399–434 | DOI | MR | Zbl

[6] Bang H. H., “Investigation of the properties of functions in the space $N_\Phi$ depending on the geometry of their spectrum”, Dolk. Akad. Nauk, 374 (2000), 590–593 (in Russian) | MR | Zbl

[7] Bang H. H., “On inequalities of Bohr and Bernstein”, J. Inequal. Appl., 7 (2002), 349–366 | DOI | MR | Zbl

[8] Bang H. H., Morimoto M., “On the Bernstein–Nikolsky inequality”, Tokyo J. Math., 14 (1991), 231–238 | DOI | MR | Zbl

[9] Bang H. H., “The sequence of Luxemburg norms of derivatives”, Tokyo J. Math., 17 (1994), 141–147 | DOI | MR | Zbl

[10] Betancor J. J., Betancor J. D., Méndez J. M. R., “Paley–Wiener type theorems for Chébli–Trimèche transforms”, Publ. Math. Debrecen, 60 (2002), 347–358 | MR | Zbl

[11] Hörmander L., “A new generalization of an inequality of Bohr”, Math. Scand., 2 (1954), 33–45 | MR | Zbl

[12] Hörmander L., The Analysis of Linear Partial Differential Operators, v. I, Springer-Verlag, Berlin etc., 1983

[13] Nessel R. J., Wilmes G., “Nilkolskii-type inequalities for trigonometric polynomials and entire functions of exponential type”, J. Austral. Math. Soc. Ser. A, 25 (1978), 7–18 | DOI | MR | Zbl

[14] Nikolskiĭ S. M., Approximation of Functions of Several Variables and Imbedding Theorems, Nauka, Moskow, 1977 (Russian) | MR

[15] Schwartz L., Théorie des Distributions, v. II, Hermann, Paris, 1951 | MR | Zbl

[16] Triebel H., Theory of Function Spaces, Birkhäuser, Basel etc., 1983 | MR | Zbl

[17] Hunt R. A., “On $L(p,q)$ spaces”, L'Ens. Math., 12 (1964), 249–275 | MR

[18] Bennett C., Sharpley R., Interpolation of Operators, 129, Academic press, New York etc., 1988 | MR | Zbl

[19] Carro M. J., Soria J., “The Hardy–Littlewood maximal function and weighted Lorentz spaces”, J. London Math. Soc., 55 (1997), 146–158 | DOI | MR | Zbl

[20] Creekmore J., “Type and cotype in Lorentz $L_{pq}$ spaces”, Indag. Math., 43 (1981), 145–152 | MR | Zbl

[21] Lorentz G. G., “Some new functional spaces”, Ann. Math., 51 (1950), 37–55 | DOI | MR | Zbl

[22] Yap L. Y. H., “Some remarks on convolution operators and $L(p,q) $ spaces”, Duke Math. J., 36 (1969), 647–658 | DOI | MR | Zbl