Inequality of Nikolsky and Bernshteins's Type Classification

Inequality of Nikolsky and Bernshteins's Type Classification

Authors

  • Alaa Radhi Makki Mirmas Department of Mathematics, Gulistan State University, Gulistan, 120100, Uzbekistan
  • Ikhlas Muhammed Nati Al. Abedi Department of Mathematics, Gulistan State University, Gulistan, 120100, Uzbekistan

DOI:

https://doi.org/10.53469/wjimt.2023.06(06).03

Keywords:

Space, Inequality Nokolsiy, Bernstein

Abstract

In this work, we learned about analytical functions in the upper half plane. Therefore, the gauge inequalities for Hardy spaces are obtained, which are similar to some of the inequalities proposed by S.M. Nokolsiy and S.N. Bernstein.

References

Nikolskiy S.M. Approximation function many variable and theorems of the embedding. M.: Nauka, 1969. -480 p.

Gaymnazarov G. Some inequality in space . Dokl. AN Tadzh, 1985. –V. 28. - №12. –p. 685-687.

Gaimnazarov G., Gaimnazarov O.G. On some inequalities for functions having derivative of fractional order. Reports of Academy of Sciences Republic of Uzbekistan, 2011, No 2, pp. 16-21.

Gaymnazarov G. About module of smoothness of the fractional order function, given on the whole material axis. Dokl. AN Tadzh., 1981. -V. 24. - 3. -p. 148-149.

G. Gaimnazarov, H. Narjigitov and O. G. Gaimnazarov On some properties of function associated with derivative of fractional order in space of Lp(-∞,∞). Far East Journal of Mathematical Sciences (FJMS) Volume 76, Number 2, 2013, pp 319-336.

Hardy G.H., Littlewood J. E . Some properties of conjugate functions. j. reinе and аngеw. Moth 1931, v167. p. 405-423.

Helle E., Tamarkin J. On the absolute integrality of Fourier transforms. Fundam. Math, v.25, 1935, p.329-351.

M. F. Timan, “The imbedding of the classes of functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1974, no. 10, 61–74.

Hardy G.Н. and Littlewoods J.E. Theorems concerning Сezaro means of pоwеr series. Рrоc, London Math. Soc.1934, V36 .p 516-531 .

Yu. A. Brudnyi, I. E. Gopengauz, “Generalization of a theorem of Hardy and Littlewood”, Mat. Sb. (N.S.), 52(94):3 (1960), 891–894.

Storozhenko Z.A., Valashek YA. Generalization of one theorem Hardi-Littllwoods. In book Constructive theory function-81.- Works to international conference on constructive theory function. -Varna, June 1-5, 1981. -Sophia: BAN, 1983.-p.164-167.

Krilov V.I. About function, the regular semi planes in floor. Mathem.sb.,1939.-V.6.-№1.-p. 95-137.

R. R. Akopyan, “Approximation of the Hardy–Sobolev class of functions analytic in a half-plane by entire functions of exponential type”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 4, 2010, 18–30.

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Published

2023-12-29
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