Geodesic
On the growth rate of arbitrary sequences of double rectangular Fourier sums
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 31-37
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The theorem is proved that an arbitrary sequence $\{S_{m_k,n_k}(f,x,y)\} _{k=1}^\infty$ of double rectangular Fourier sums of any function from the class $L(\ln^+L)^2([0,2\pi)^2)$ satisfies almost everywhere the relation $S_{m_k,n_k}(f,x,y)=o(\ln k)$.
Keywords: multiple trigonometric Fourier series, almost everywhere convergence. 
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N. Yu. Antonov. On the growth rate of arbitrary sequences of double rectangular Fourier sums. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 31-37. http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a2/

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