Limit properties of one class of functions that are harmonic in a circle

Poddubny Oleksiy Mykhailovych

Poddubny Oleksiy Mykhailovych ¹

¹ Department of Function Theory and Mathematics Teaching Methods, Lesya Ukrainka Eastern European National University, Volyn, Lutsk, 43025, Ukraine

Keywords: limit properties, Hardy–Littlewood theorem

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Abstract

In this paper we study the boundary behavior of harmonic functions in the unit disc of the complex plane. The obtained results generalize some Stegbuchner results and are analogous to the well-known Hardy–Littlewood theorem.

References

[1] Hardy G., Littlewood J. E. Some properties of fractional integrals. II // Math. Zeitschr. – 1931. – 34. – P. 403-439.

[2] Kovalchuk R. N. On some properties of the integral modulus of smoothness of the boundary function of the class $H_p (p ≥ 1)$ // Theor. of Functions, Functional Analysis and Appl. 1969. 6. P. 14 - 20.

[3] Nikolskii S. M. Fourier series with a given continuity module // Dokl. of the USSR Academy of Sciences 1946. 52, № 3 P. 191 - 194.

[4] Bari N.K., Stechkin S.B. Best approximations and differential properties of two conjugate functions // Proceedings of the Mosc. Mathematical Society 1956. 5. P. 483 - 522.

[5] Stegbuchner H. On some extensions of a theorem of Hardy and Littlewood // Ann. Acad. Sci. Fenn. Ser. A I Math. - 1982. - 7, № 2. - P. 113 – 117.

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Cite

ACS Style: Poddubny, O.M. Limit properties of one class of functions that are harmonic in a circle. Bukovinian Mathematical Journal. 2016, 2
AMA Style: Poddubny OM. Limit properties of one class of functions that are harmonic in a circle. Bukovinian Mathematical Journal. 2016; 2(2-3).
Chicago/Turabian Style: Oleksiy Mykhailovych Poddubny. 2016. "Limit properties of one class of functions that are harmonic in a circle". Bukovinian Mathematical Journal. 2 no. 2-3.

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