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DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

Behaviour of exponential means of Fourier series and conjugated Fourier series in Lebesgue points

Vestnik MGSU 10/2014
  • Osilenker Boris Petrovich - Moscow State University of Civil Engineering (MGSU) Doctor of Physical and Mathematical Sciences, Professor, Professor, Department of Higher Mathematics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Nakhman Aleksandr Davidovich - Tambov State Technical University (TSTU) Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Applied Mathematics and Mechanics, Tambov State Technical University (TSTU), 106 Sovetskaya, Tambov, 392000, Russian Federation; +7 (4752) 72-66-72; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 54-63

In the present paper the researches consider the behavior of the class of operators defined by exponential summing methods of Fourier series. The authors examine exponential means of certain Fourier series. The convergence in Lebesgue points is investigated. The operators determined by the convergence are known as the means of Poisson - Abel and they play the substantial role in different questions of the analysis. Though even the most simple and natural extension is not fully investigated. Conclusions of the considered theorem follow from the results for general infinite convex or piecewise convex summing sequences; the given results are also of individual interest. The analogue of the theorem is specified for exponential means of conjugate Fourier series. The examples of exponential means are given, which satisfy the hypotheses of the considered theorems and are also of individual interest. The obtained results are valid, in particular, for the generalized Poisson means. The authors also give an example of a polynomial-exponential method of summation.

DOI: 10.22227/1997-0935.2014.10.54-63

References
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  8. Trigub R.M. Lineynye metody summirovaniya i absolyutnaya skhodimost' ryadov Fur'e [Linear Summation Methods and Absolute Convergence of Fourier Series]. Izvestiya AN SSSR. Seriya matematicheskaya [News of the Academy of Sciences of the USSR. Mathematical Series]. 1968, vol. 32, no. 1, pp. 24—29. (in Russian)
  9. Dyn'kin E.M., Osilenker B.P. Vesovye otsenki singulyarnykh integralov i ikh prilozheniya [Weighted Estimates for Singular Integrals and their Applications]. Itogi nauki i tekhniki : Seriya Matematicheskiy Analiz [Totals of Science and Technology. Series: Mathematical Analisys]. Moscow, VINITI Publ., 1983, vol. 21, pp. 42—129. (in Russian)
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