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

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.