Abstract
We investigate the convergence behavior of the family of double sine integrals of the form $$\int^\infty_0 \int^\infty_0 f(x,y) \sin ux \sin vy\, dx\, dy, \quad \hbox{where} \quad (u,v) \in \mathbb R^2_+: = \mathbb R_+ \times \mathbb R_+, $$ $\mathbb R
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