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

We establish a general sufficient condition for the possibility of representation of functions f max x 1 x 2 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...

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Veröffentlicht in:Ukrainian mathematical journal 2016, Vol.67 (8), p.1219-1235
Hauptverfasser: Kotova, O. V., Trigub, R. M.
Format: Artikel
Sprache:eng
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Zusammenfassung:We establish a general sufficient condition for the possibility of representation of functions f max x 1 x 2 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.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-016-1147-z