CONVERGENCE ALMOST EVERYWHERE OF CERTAIN PARTIAL SUMS OF FOURIER INTEGRALS
Published online by Cambridge University Press: 20 March 2003
Abstract
Suppose that $R$ goes to infinity through a second-order lacunary set. Let $S_R$ denote the $R$th spherical partial inverse Fourier integral on ${\rm I\!R}^d$. Then $S_R f$ converges almost everywhere to $f$, provided that $f$ satisfies \[ \int \widehat{f}(\xi)\log\log(8+|\xi|)^2\,d\xi < \infty. \]
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