Bernstein - Nikolskii type inequality in Lorentz spaces and related topics
Автор: Bang Ha Huy, Cong Nguyen Minh
Журнал: Владикавказский математический журнал @vmj-ru
Статья в выпуске: 2 т.7, 2005 года.
Бесплатный доступ
In this paper we study the Bernstein - Nikolskii type inequality, the inverse Bernstein theorem and some properties of functions and their spectrum in Lorentz spaces L^{p,q}(\R^n).
Короткий адрес: https://sciup.org/14318150
IDR: 14318150
Список литературы Bernstein - Nikolskii type inequality in Lorentz spaces and related topics
- Bang H. H. A property of infinitely differentiable functions//Proc. Amer. Math. Soc.-1990.-V. 108.-P. 71-78.
- Bang H. H. On the Bernstein-Nikolsky inequality II//Tokyo J. Math.-1995.-V. 19.-P. 123-151.
- Bang H. H. Functions with bounded spectrum//Trans. Amer. Math. Soc.-1995.-V. 347.-P. 1067-1080.
- Bang H. H. Spectrum of functions in Orlicz spaces//J. Math. Sci. Univ. Tokyo.-1997.-V. 4.-P. 341-349.
- Bang H. H. The study of the properties of functions belonging to an Orlicz space depending on the geometry of their spectra (Russian)//Izv. Russ. Akad. Nauk Ser. Mat.-1997.-V. 61.-P. 163-198; translation in Izv. Math.-V. 61.-P. 399-434.
- Bang H. H. Investigation of the properties of functions in the space N_\Phi depending on the geometry of their spectrum (Russian)//Dolk. Akad. Nauk.-2000.-V. 374.-P. 590-593.
- Bang H. H. On inequalities of Bohr and Bernstein//J. Inequal. Appl.-2002.-V. 7.-P. 349-366.
- Bang H. H. and Morimoto M. On the Bernstein -Nikolsky inequality//Tokyo J. Math.-1991.-V. 14.-P. 231-238.
- Bang H. H. The sequence of Luxemburg norms of derivatives//Tokyo J. Math.-1994.-V. 17.-P. 141-147.
- Betancor J. J., Betancor J. D., Mendez J. M. R. Paley -Wiener type theorems for Chebli -Trimeche transforms//Publ. Math. Debrecen.-2002.-V. 60.-P. 347-358.
- Hormander L. A new generalization of an inequality of Bohr//Math. Scand.-1954.-V. 2.-P. 33-45.
- Hormander L. The Analysis of Linear Partial Differential Operators I.-Berlin etc.: Springer-Verlag, 1983.
- Nessel R. J., Wilmes G. Nilkolskii-type inequalities for trigonometric polynomials and entire functions of exponential type//J. Austral. Math. Soc. Ser. A.-1978.-V. 25.-P. 7-18.
- Nikolskii S. M. Approximation of Functions of Several Variables and Imbedding Theorems.-Moskow: Nauka, 1977. [Russian]
- Schwartz L. Theorie des Distributions II.-Paris: Hermann, 1951.
- Triebel H. Theory of Function Spaces.-Basel etc.: Birkhauser, 1983.
- Hunt R. A. On L(p,q) spaces//L'Ens. Math.-1964.-V. 12.-P. 249-275.
- Bennett C., Sharpley R. Interpolation of Operators.-New York etc.: Academic press, 1988.
- Carro M. J., Soria J. The Hardy -Littlewood maximal function and weighted Lorentz spaces//J. London Math. Soc.-1997.-V. 55.-P. 146-158.
- Creekmore J. Type and cotype in Lorentz L_{pq} spaces//Indag. Math.-1981.-V. 43.-P. 145-152.
- Lorentz G. G. Some new functional spaces//Ann. Math.-1950.-V. 51.-P. 37-55.
- Yap L. Y. H. Some remarks on convolution operators and L(p,q) spaces//Duke Math. J.-1969.-V. 36.-P. 647-658.
Статья научная
