2017
Том 69
№ 6

All Issues

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

Kotova O. V., Trigub R. M.


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.

English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 8, pp 1219-1235.

Citation Example: Kotova O. V., Trigub R. 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 // Ukr. Mat. Zh. - 2015. - 67, № 8. - pp. 1082-1096.