On the boundedness of pseudodifferential operators in Hölder-Zygmund spaces

Authors

  • Kryakvin V.D. Southern Federal University, Rostov-on-Don, Russian Federation
  • Omarova G.P. Southern Federal University, Rostov-on-Don, Russian Federation

UDC

517.9

Abstract

A recent result on the boundedness of pseudodifferential operators in the scale of Hölder-Zygmund spaces is specified in the present article. Upper bound of the operator norm is presented.

Keywords:

pseudodifferential operators, Hölder-Zygmund spaces

Author info

  • Vadim D. Kryakvin

    канд. физ.-мат. наук, доцент кафедры алгебры и дискретной математики Южного федерального университета

  • Gulnara P. Omarova

    магистрант кафедры алгебры и дискретной математики Южного федерального университета

References

  1. Stein E.M. Harmonic analysis: real-variable methods, orthogonality and oscillatory integrals. Princeton: Princeton University Press, 1993. 685 pp.
  2. Стейн И.М. Сингулярные интегралы и дифференциальные свойства функций. М.: Мир, 1973. 343 c.
  3. Yan Lin, Shan Zhen Lu Pseudo-differential operators on Sobolev and Lipschitz spases // Acta Mathematica Sinica. 2010. Vol. 26. No 1. P. 131-142.
  4. Beals R. $L^p$ and Holder estimates for pseudodifferential operators:sufficient conditions // Ann. Inst. Fourier. 1979. Vol. 29. No 3 P. 239-260.
  5. Rabinovich V.S. Fredholm property of pseudo-differential operators on weighted Hölder-Zygmund spaces // Operator Theory: Advances and Applications. 2006. Vol. 164. P. 95-114.
  6. Кряквин В. Д. Критерии компактности и нетеровости псевдодифференциальных операторов в весовых пространствах Гельдера-Зигмунда // Дифф. уравнения. 2009. №1. C. 101-110.

Downloads

Download data is not yet available.

Issue

Pages

45-48

Section

Article

Dates

Submitted

December 1, 2011

Accepted

December 8, 2011

Published

December 23, 2011

How to Cite

[1]
Kryakvin, V.D., Omarova, G.P., On the boundedness of pseudodifferential operators in Hölder-Zygmund spaces. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2011, № 4, pp. 45–48.

Similar Articles

1-10 of 57

You may also start an advanced similarity search for this article.