A New Sufficient Condition for Belonging to the Algebra of Absolutely Convergent Fourier Integrals and Its Application to the Problems of Summability of Double Fourier Series

  • O. V. Kotova Донец. нац. ун-т
  • R. M. Trigub Донец. нац. ун-т

Abstract

We establish a general sufficient condition for the possibility of representation of functions $$f\left( \max \left\{\left|{x}_1\right|,\left|{x}_2\right|\right\}\right)$$ in the form of absolutely convergent double Fourier integrals and study the possibility of its application to various problems of summability of double Fourier series, in particular, by using the Marcinkiewicz–Riesz method.
Published
25.08.2015
How to Cite
KotovaO. V., and TrigubR. M. “A New Sufficient Condition for Belonging to the Algebra of Absolutely Convergent Fourier Integrals and Its Application to the Problems of Summability of Double Fourier Series”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 8, Aug. 2015, pp. 1082-96, http://umj.imath.kiev.ua/index.php/umj/article/view/2047.
Section
Research articles